Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Shape of the universe wikipedia , lookup
Analytic geometry wikipedia , lookup
Cartan connection wikipedia , lookup
Integer triangle wikipedia , lookup
Rational trigonometry wikipedia , lookup
Algebraic geometry wikipedia , lookup
Pythagorean theorem wikipedia , lookup
Geometrization conjecture wikipedia , lookup
Line (geometry) wikipedia , lookup
Geometry EOI Practice PASS 1.1: Identify and use logical reasoning skills (inductive and deductive) to make and test conjectures, formulate counter examples, and follow logical arguments. 1. By the Law of Syllogism, what statement follows from the following pair of true statements? Use the following statements for exercises 3 and 4. p: If a rectangle is a rhombus, then the rectangle is a square. q: If a rectangle is a square, then the rectangle is a rhombus. r: If a rectangle is not a rhombus, then the rectangle is not a square. s: If a rectangle is not a square, then the rectangle is not a rhombus. 1.1 If Nate eats chips, then he uses salsa dip. If Nate uses salsa dip, then he gets indigestion. a. Nate uses salsa dip. b. Nate gets indigestion. c. If Nate uses salsa dip, then he gets indigestion. d. If Nate eats chips, then he gets indigestion. 3. Which statement is truth 1.1 functionally equivalent to q? a. p c. s b. r d. none 2. Which statement is logically 1.1 equivalent to the statement, “If we recycle, then the amount of trash in landfills is reduced”? a. If we do not recycle, then the amount of trash in landfills is not reduced. b. If the amount of trash in landfills is reduced, then we recycled. c. If the amount of trash in landfills is not reduced, then we did not recycle. d. If we do not recycle, then the amount of trash in landfills is reduced. Moore Public Schools Geometry EOI Practice 4. Which statements are true? a. p and s only c. none b. q and r only d. all 1.1 1 Geometry EOI Practice 5. What logical conclusion can 1.1 be made from the following statements? 7. Use the statement below to 1.1 answer the following question. • If Delphie has sugar in her cupboard, then she can make apple pie. • Delphie has sugar in her cupboard. • All fruits grow on trees. Which proves the statement false? a. Oranges are fruits. Oranges grow on trees. b. Acorns grow on trees. Acorns are not fruits. c. Strawberries are fruits. Strawberries do not grow on trees. d. Potatoes are not fruits. Potatoes do not grow on trees. a. Delphie just bought some sugar. b. Apples make good pie. c. Delphie can make apple pie. d. Apple pie is made with sugar 6. The following statements are 1.1 true: 8. Make a conjecture about the 1.1 next term in this sequence: 92, 87, 82, 77, 72. • If the phone rings, Antoine will answer it. • If Antoine answers the phone, he will have to take a message. • Antoine has not taken any messages. a. -5 b. 62 Which statements must be true? 9. Given: a + b ≤ 8and a = 2 1.1 Conjecture: b ≤ 5 a. The phone has not rung. b. Antoine does not have any paper. c. Antoine has answered the phone. d. The phone has been busy all day. Moore Public Schools Geometry EOI Practice c. 67 d. 77 Which of the following would be a counterexample? a. b = 3 b. b = 5 2 c. b = 6 d. b = a Geometry EOI Practice 12. Marcus is on the track team. 1.1 He participates in the high jump and the 100-meter race, but does not participate in the 4-person relay. In which section of the diagram below should Marcus be placed? 10. “Two lines in a plane 1.1 always intersect in exactly one point.” Which of the following best describes a counterexample to the assertion above? a. Coplanar lines b. Parallel lines c. Perpendicular lines d. Intersecting lines 11. Which figure can serve as a 1.1 counterexample to the conjecture below? • If one pair of opposite sides of a quadrilateral is parallel, then the quadrilateral is a parallelogram. a. Rectangle b. Rhombus c. Square d. Trapezoid Moore Public Schools Geometry EOI Practice 3 a. A b. B c. C d. D a. A c. C b. B d. D Geometry EOI Practice 13. Alice, Bob, Colleen, and 1.1 Dave are in line at a grocery store. Each needs to buy a different item. The items are bread, cereal, milk, and fruit. 14. Jeff, Kim, Hans, and Lou 1.1 each have a different pet: a dog, a turtle, a parrot, and a snake. Jeff is teaching his pet to speak. Kim’s pet has four legs. Hans’ pet has no legs. Lou’s pet has more legs than Jeff’s pet but no fur. Who owns the dog? 1. Bob was second inline, after the person who bought milk but before the person who bought the bread. 2. Colleen did not buy the fruit. 3. Alice bought the cereal. 4. Dave was the first person in line. Based on the statements, who bought the loaf of bread? a. Alice c. Colleen b. Bob d. Dave Moore Public Schools Geometry EOI Practice 4 a. Jeff c. Hans b. Kim d. Lou Geometry EOI Practice PASS 1.2: State, use, and examine the validity of the converse, inverse, and contrapositive of “if-then” statements. 1. Which statement is the 1.2 converse of a → b ? 4. Which statement is the 1.2 inverse of “If it rains, then I do not go fishing”? a. b → a b. a → ∼ b c. ∼ a → ∼ b d. ∼ b → ∼ a a. If I do not go fishing, then it rains. b. If it does not rain, then I go fishing. c. If it rains, then I go fishing. d. If I go fishing, then it does not rain. 2. What is the converse of the 1.2 statement “If x is even, then x + 1 is odd”? 5. What is the contrapositive of 1.2 the statement q → ∼ p ? a. If y is even, then y + 1 is odd. b. If x is not even, then x + 1 is odd. c. If x is odd, then x + 1 is even. d. If x + 1 is odd, then x is even. a. b. c. d. ∼ p→q p→ ∼q 6. Which is the contrapositive 1.2 of ∼ p → q ? 3. Which is the converse of the 1.2 statement “If today is Presidents’ Day, then there is no school”? a. b. c. d. a. If today is Presidents’ Day, then there is school. b. If there is school, then today is not Presidents’ Day. c. If there is no school, then today is Presidents’ Day. d. If today is not Presidents’ Day, then there is school. Moore Public Schools Geometry EOI Practice ∼q→ p ∼ p→q 5 ∼q→ p p→ ∼q q→ ∼ p ∼ p↔q Geometry EOI Practice Use the following statements for exercises 7-10. p: If a rectangle is a rhombus, then the rectangle is a square. q: If a rectangle is a square , then the rectangle is a rhombus. r: If a rectangle is not a rhombus, then the rectangle is not a square. s: If a rectangle is not a square, then the rectangle is not a rhombus. 7. Which statement is the 1.2 inverse of p? a. p b. q 9. Which statement is the 1.2 contrapositive of q? c. r d. s a. p b. q 8. Which statement is the contrapositive of p? 10. Which statement is the 1.2 inverse of r? 1.2 a. p b. q Moore Public Schools Geometry EOI Practice c. r d. s c. r d. s a. p b. q 6 c. r d. s Geometry EOI Practice PASS 2.2a: Use the angle relationships formed by parallel lines cut by a transversal to solve problems. 4. Given For Questions 1-5, refer to the following figure. Identify the special name for each angle pair. 2.2a s t and m∠1 = 8 x − 4 and m∠15 = 6 x + 24, find x. a. -10 b. 14 5. If s t by the Alternate Exterior 2.2a Angles Theorem, which angle pair must be congruent? 1. ∠1 and ∠5 a. ∠1 and ∠7 b. ∠1 and ∠5 2.2a a. b. c. d. c. 20 d. 28 alternate exterior alternate interior consecutive interior corresponding c. ∠1 and ∠15 d. ∠1 and ∠13 6. Which of the following is not 2.2a true when a b ? Refer to the following figure. 2. ∠10 and ∠14 2.2a a. b. c. d. alternate exterior alternate interior consecutive interior corresponding a. b. c. d. 3. Given s t and m∠7 = 84, find m∠10. 2.2a a. 6 b. 84 Moore Public Schools Geometry EOI Practice c. 96 d. 104 7 ∠1 ≅ ∠5 and ∠4 ≅ ∠8 m∠2 = m∠6 m∠1 + m∠5 = 180° m∠4 + m∠6 = 180° Geometry EOI Practice 7. Which of the statements must be 2.2a true if a b and x y ? Refer to the following figure. 9. In the figure shown below, lines 2.2a l and m are parallel. I. m∠1 = m∠5 II. m∠3 + m∠5 = 180° III. m∠7 + m∠8 = 180° What is the value of x? a. I only b. II only a. 20° b. 60° c. III only d. I and III 8. If m∠4 = 50° and b c , then which 2.2a statement is true? Refer to the following figure. a. m∠6 = m∠10 b. m∠8 = 50° 10. In the figure shown below, 2.2a lines l and m are parallel and line t is a transversal. Which pair of angles must be supplementary? c. m∠8 = m∠7 d. m∠6 = 60° a. ∠1 and ∠6 b. ∠3 and ∠5 Moore Public Schools Geometry EOI Practice c. 80° d. 100° 8 c. ∠3 and ∠7 d. ∠4 and ∠5 Geometry EOI Practice 11. A construction engineer needs to make sure a ceiling beam is parallel to 2.2a its corresponding floor beam. Using the drawing below as a guide, which pair of measurements is sufficient to show the beams are parallel? Which pair of angles must be supplementary? a. x = z b. y = w Moore Public Schools Geometry EOI Practice c. x = y d. y = z 9 Geometry EOI Practice PASS 2.2b: Use the angle relationships formed by two lines cut by a transversal to determine if the two lines are parallel and verify, using algebraic and deductive proofs. 3. If m∠6 = 10 x − 6 and m∠11 = 4 x + 18, 2.2b find x so that s t. For Questions 1-3, refer to the figure below. Identify the special name for each angle pair. a. 2 b. 4 c. 12 d. 32 4. Which postulate or theorem y. 2.2b would prove x 1. Given ∠6 ≅ ∠12, which postulate 2.2b or theorem justifies that s t ? a. Corresponding Angles Postulate b. Consecutive Interior Angles Theorem c. Alternate Exterior Angles Theorem d. Alternate Interior Angles Theorem a. Consecutive Interior Angles Converse b. Corresponding Angles Converse c. Alternate Interior Angles Converse d. Alternate Exterior Angles Converse 2. If ∠8 ≅ ∠16, which postulate or 2.2b theorem justifies that s t ? a. Corresponding Angles Postulate b. Consecutive Interior Angles Theorem c. Alternate Exterior Angles Theorem d. Alternate Interior Angles Theorem Moore Public Schools Geometry EOI Practice 10 Geometry EOI Practice 5. Which postulate or theorem y. 2.2b would prove x 7. Which lines are parallel? 2.2b a. Consecutive Interior Angles Converse b. Alternate Interior Angles Converse c. Alternate Exterior Angles Converse d. Cannot prove x y with given information a. EB FD c. EF BC b. AE CF d. both b and c 8. Complete the following to make 2.2b a true statement. “In a plane, if two lines are _?_ to the same line, then they are _?_ to each other.” a. b. c. d. 6. What value of x would make 2.2b lines w and v parallel? perpendicular, parallel perpendicular, perpendicular parallel, parallel both a and c 9. Determine which lines must be 2.2b parallel. a. 30 b. 20 c. 60 d. 40 a. a b b. c d Moore Public Schools Geometry EOI Practice 11 c. c e d. both a and c Geometry EOI Practice Use the figure below for Exercises 12-13. 10. What value of x makes a b ? 2.2b a. 10 b. 30 c. 50 d. 70 12. If m∠1 = m∠9, then which two 2.2b lines are parallel? 11. Which best describes the 2.2b relationship of the lines shown below? a. b d b. b c c. a d d. c d 13. If m∠6 = 85° and m∠4 = 95° , 2.2b then the following conclusion can be made: a. a ⊥ d b. b c a. a ⊥ b b. c a Moore Public Schools Geometry EOI Practice c. b a d. b c 12 c. d c d. b d Geometry EOI Practice PASS 2.2c: Use relationships between pairs of angles (for example, adjacent, complementary, vertical) to solve problems. 1. Find m∠BDC. 4. Which angles are 2.2c supplementary? 2.2c a. ∠1 and ∠4 b. ∠4 and ∠5 a. 185° b. 115° c. 25° d. 175° c. ∠1 and ∠5 d. B and C 5. What is the m∠1? 2.2c Refer to the diagram below for Exercises 2-4. a. 45° b. 90° c. 55° d. 145° 6. Find the value of x. 2.2c 2. Which angles are a linear pair? 2.2c a. ∠1 and ∠2 b. ∠2 and ∠3 c. ∠1 and ∠4 d. ∠4 and ∠5 a. 13.3 b. 7 7. Two angles are 2.2c complementary. One angle has a measure that is twice the other angle. What is the measure of the smaller angle? 3. Which angles are vertical 2.2c angles? a. ∠1 and ∠2 b. ∠1 and ∠5 c. ∠3 and ∠5 d. ∠1 and ∠4 a. 15 b. 30 Moore Public Schools Geometry EOI Practice c. 14 d. 26 13 c. 45 d. 60 Geometry EOI Practice 11. If m∠ABD = 56, find m∠DBC . 8. Find the value of y. 2.2c 2.2c a. 10 b. 28 c. 20 d. 152 a. 124 b. 56 9. What is the measure of 2.2c the diagram? a. 3° b. 39° ∠x in 12. If m∠AFB = 5 x − 10 and 2.2c m∠BFC = 3 x + 20, find x . c. 5° d. 65° a. 10 b. 15 right complementary vertical supplementary Moore Public Schools Geometry EOI Practice c. 21.25 d. 23.3 13. Two boards are being cut at 2.2c angles to ensure a tight fit. If one board is cut at a 140° angle, what must the acute angle of the other board measure to form the tight fit? 10. To solve for x, what angle 2.2c relationship would you use? a. b. c. d. c. 44 d. 34 a. 40° b. 90° 14 c. 60° d. 140° Geometry EOI Practice 17. Which pair of angles are not 2.2c adjacent? For Questions 14-16, use the figure below a. ∠1and ∠2 b. ∠3 and ∠4 14. Which pair of angles are 2.2c vertical angles? a. b. c. d. ∠RST , ∠TSU ∠RSX , ∠TSU ∠TSU , ∠USV ∠RSX , ∠XSW 18. Use the diagram to find 2.2c m∠FDG. 15. Which angle is 2.2c supplementary to ∠USV ? a. ∠TSU b. ∠VSW c. ∠2 and ∠3 d. ∠1 and ∠4 a. 15° b. 120° c. ∠RSV d. ∠WSR c. 150° d. 130° 19. In the diagram, what are the 2.2c values of x and y? 16. Find x and y. 2.2c a. b. c. d. x = 10, y = 12 x = 20, y = 7 x = 10, y = 8 x = 50, y = 40 Moore Public Schools Geometry EOI Practice a. x = 47, y = 75 b. x = 47, y = 74 15 c. x = 75, y = 47 d. x = 71, y = 51 Geometry EOI Practice PASS 2.3a: Identify, describe, and analyze polygons (for example, convex, concave, regular, pentagonal, hexagonal, n-gonal). 1. A triangle with three acute 2.3a angles and no congruent sides is _?_ . a. b. c. d. 4. The triangle below can be 2.3a classified as _?_ . an equiangular triangle a right triangle an isosceles triangle an acute scalene triangle a. b. c. d. 2. A triangle with side lengths 2.3a of 5 cm, 3 cm, and 5 cm is _?_ . a. b. c. d. an equilateral triangle an obtuse triangle an isosceles triangle an acute triangle acute isosceles acute scalene obtuse isosceles obtuse scalene 5. Which of the following is not 2.3a a polygon? 3. The triangle below can be 2.3a classified as _?_ . a. c. b. d. 6. A polygon with seven sides is 2.3a called a(n) a. b. c. d. a. octagon b. decagon acute isosceles acute scalene obtuse isosceles obtuse scalene 7. If a polygon is both 2.3a equiangular and equilateral, how should it be classified? a. regular b. right Moore Public Schools Geometry EOI Practice c. heptagon d. hexagon 16 c. congruent d. irregular Geometry EOI Practice 8. Which describes this figure? 11. Which figure is not a 2.3a polygon? 2.3a a. a. hexagon, concave, not regular b. pentagon, concave, regular c. hexagon, convex, not regular d. not a polygon b. c. d. 12. Which figure is not a 2.3a convex polygon? a. b. c. d. 9. If m∠L = 45 and m∠M = 45, LMN 2.3a is classified as what kind of triangle? a. b. c. d. 13. Which figure is not a 2.3a regular polygon? acute scalene obtuse isosceles acute isosceles right isosceles a. 10. The figure shown below can 2.3a be classified as which of the following? a polygon II. a quadrilateral III. a hexagon IV. an octagon I. a. b. c. d. I, II, IV II III I, IV Moore Public Schools Geometry EOI Practice 17 b. c. d. Geometry EOI Practice 14. The figure is an example of 2.3a _?_ . a. hexagon b. heptagon Moore Public Schools Geometry EOI Practice 15. What type of triangle is ABC ? 2.3a a. b. c. d. c. octagon d. nonagon 18 acute isosceles right scalene right isosceles obtuse scalene Geometry EOI Practice PASS 2.3b: Apply the interior and exterior angle sum of convex polygons to solve problems, and verify using algebraic and deductive proofs. 4. What is the measure of an 2.3b exterior angle of regular pentagon? 1. An exterior angle at the base 2.3b of an isosceles triangle measures 110°. What is the measure of the vertex angle? a. 55° b. 110° a. 51.4° b. 72° c. 108° d. 144° c. 70° d. 40° 5. Find the measure of ∠A . 2.3b 2. Each exterior angle of a 2.3b certain regular polygon measures 30°. How many sides does the polygon have? a. 6 b. 9 c. 10 d. 12 a. 45° b. 55° 6. The diagram below has a 2.3b triangular area. What are the measures of the 3 angles inside the triangle? 3. What is the measure of ∠A in 2.3b the regular polygon? a. 45° b. 120° Moore Public Schools Geometry EOI Practice c. 58° d. 85° c. 135° d. 145° a. b. c. d. 19 90°, 50°, 40° 90°, 60°, 30° 90°, 45°, 45° 110°, 50°, 20° Geometry EOI Practice 7. A regular polygon has an 2.3b interior angle with a measure of 135°. How many sides does the polygon have? a. 5 b. 6 11. In triangle ABC shown 2.3b below, m∠A = 60° and m∠C=80°. The exterior angle at B measures (x + 10)°. What is the value of x? c. 7 d. 8 8. What is the value x? 2.3b a. 30 b. 50 a. 45 b. 50 12. Mary is designing a garden 2.3b in the shape of a regular octagon. She intends to surround the garden with a border of rocks as shown in the figure below. At what angle should the sections of the border intersect? c. 55 d. 60 9. What is the number of sides 2.3b of a polygon if the sum of the measures of its angles is 1260°? a. 5 b. 6 c. 130 d. 140 c. 7 d. 9 10. What is the number of sides 2.3b of a polygon if the sum of the measures of its angles is 4140°? a. 25 b. 23 Moore Public Schools Geometry EOI Practice a. 45° b. 60° c. 21 d. 24 20 c. 120° d. 135° Geometry EOI Practice 16. What are the values of x, 2.3b and y? 13. What is the sum of the 2.3b measures of the exterior angles of a decagon? a. 1440° b. 1080° c. 360° d. 720° 14. Find the sum of the 2.3b measures of the interior angles of a convex 50-gon. a. 9000 b. 8640 a. b. c. d. c. 360 d. 172.8 15. Find x. x = 91°, y = 98° x = 91°, y = 108° x = 101°, y = 98° x = 101°, y = 108° 17. In the diagram, 2.3b ∆ABC and ∆RST are congruent equilateral triangles with corresponding sides parallel. 2.3b What is the value of x? a. 16 b. 34 c. 50 d. 70 a. 90° b. 120° Moore Public Schools Geometry EOI Practice 21 c. 135° d. 144° Geometry EOI Practice 18. The measures of some 2.3b angles are given in this figure. What is the measure of ∠N ? a. 40° b. 58° 20. Figure ABCDEFGH is a 2.3b regular octagon. What is the measure of ∠DCQ ? c. 82° d. 122° a. 135° b. 60° 19. In the figure, the measure of 2.3b ∠CAD is twice the measure of ∠CAB . What is the measure of ∠CAB ? a. 120° b. 60° Moore Public Schools Geometry EOI Practice c. 45° d. 30° 21. The measures of some 2.3b angles are given in the figure. What is the value of x? c. 45° d. 30° a. 65 b. 70 22 c. 80 d. 85 Geometry EOI Practice 22. The polygon shown is 2.3b convex. The sum of its interior angle measures is _?_ 25. Find the value of x. 2.3b a. 21 b. 25 a. 900° b. 1,260° 26. The sum of the interior 2.3b angles of a polygon is the same as the sum of its exterior angles. What type of polygon is it? c. 1,620° d. 2,520° 23. Which angle measure below 2.3b is not a possible measure of an exterior angle of a regular polygon? a. 36° b. 40° c. 28 d. 31 a. quadrilateral c. octagon b. hexagon d. decagon c. 45° d. 54° 27. In the figure, TIL overlaps RAN. RIG is formed. 2.3b What is the m∠c in RIG? 24. In the figure, what is the measure of ∠C ? a. 70° b. 90° Moore Public Schools Geometry EOI Practice c. 100° d. 110° a. 30° b. 55° 23 c. 85° d. 95° Geometry EOI Practice PASS 2.3c: Develop and apply the properties of quadrilaterals to solve problems (for example, rectangles, parallelograms, rhombi, trapezoids, kites). 1. What are the values of the 2.3c variables in quadrilateral MNOP? a. b. c. d. x = 4, x = 6, x = 5, x = 7, y y y y = = = = 4. KLMN is a parallelogram. 2.3c Which of the following statements is false? 19 19 27 26 a. KP = MP b. LP = NP 5. If ∠D ≅ ∠F and ∠E and ∠F are 2.3c supplementary, then you know that DEFG must be what type of special quadrilateral? 2. NPQR is a trapezoid and ST 2.3c = 24. Find the value of x. a. 6 b. 10 c. 8 d. 9 a. parallelogram c. rhombus b. square d. rectangle 3. ABCD is a parallelogram. 2.3c Find m∠C . a. 57° b. 66° Moore Public Schools Geometry EOI Practice c. LM = KN d. LN = KM 6. Which quadrilateral is a 2.3c parallelogram? c. 76° d. 114° 24 a. c. b. d. Geometry EOI Practice 7. Which of the following terms 2.3c could not be used to describe the figure below? 10. Find m∠1 in parallelogram 2.3c ABCD. a. 19 b. 38 c. 52 d. 56 a. parallelogram c. rectangle b. square d. quadrilateral 11. ABCD is a parallelogram 2.3c with diagonals intersecting at E. If AE = 4x – 8 and EC = 36, find x. 8. What is the length of the 2.3c midsegment of trapezoid ABCD? a. 7 b. 11 a. 6 b. 8 c. 9 d. 15 c. 15.5 d. 38 12. Find x and y so that this 2.3c quadrilateral is a parallelogram. 9. Which of the following 2.3c statements is never true? a. A trapezoid is a rectangle. b. A rectangle is a parallelogram. c. A parallelogram is a rhombus. d. A square is a rhombus. Moore Public Schools Geometry EOI Practice a. b. c. d. 25 x= x= x= x= 27, 27, 13, 13, y y y y = = = = 90 40 90 40 Geometry EOI Practice 13. Find x so that this 2.3c quadrilateral is a parallelogram. a. 7 1 3 b. 8 16. EF is the median of 2.3c isosceles trapezoid ABCD. Find x. c. 12 a. 2x - 46 b. 32 d. 66 17. Given rhombus ABCD, find 2.3c m∠1. 14. The diagonals of square 2.3c ABCD intersect at E. If AE = 2x + 6 and BD = 6x – 10, find AC. a. 11 b. 28 c. 46 d. 68 c. 56 d. 90 a. 45 b. 60 c. 90 d. 120 15. For isosceles trapezoid 2.3c MNOP, find m∠MNP. 18. In trapezoid DEFG, find 2.3c m∠D. a. 44 b. 64 Moore Public Schools Geometry EOI Practice c. 80 d. 116 a. 44 b. 72 26 c. 108 d. 136 Geometry EOI Practice 19. Given trapezoid ABCD with 2.3c median EF , which of the following is true? 22. Given: TRAP is isosceles 2.3c trapezoid with diagonals RP and TA . Which of the following must be true? a. RP ⊥ TA b. RP TA a. EF = 1 2 AD b. AE = FD c. RP ≅ TA d. RP bisects TA c. AB = EF d. EF = BC + AD 23. What values of a and b 2.3c make quadrilateral MNOP a parallelogram? 2 20. Quadrilateral ABCD is a 2.3c parallelogram. Which of the following must be true? a. a = 1, b = 5 b. a = 5, b = 1 a. AB ≅ AD b. AC ≅ BD c. ∠A ≅ ∠D d. ∠B ≅ ∠D c. a = 11 d. a = 34 7 7 ,b= 34 ,b= 11 7 7 21. ABCD is a rhombus. What 2.3c is the measure of ∠CBD ? 24. Choose the statement that is 2.3c true about a kite. a. 50° b. 60° Moore Public Schools Geometry EOI Practice a. Only one pair of opposite angles are congruent. b. Opposite sides are congruent. c. Diagonals bisect each other. d. Diagonals are congruent. c. 70° d. 75° 27 Geometry EOI Practice PASS 2.3d: Use properties of 2-dimensional figures and side length, perimeter or circumference, and area to determine unknown values and correctly identify the appropriate unit of measure of each. 1. 2.3d 2. 2.3d 3. 2.3d A rectangle has an area of 150 ft 2 and a perimeter of 50 ft. What are the dimensions of the rectangle? 4. 2.3d The area of a circle is the same as the area of a square whose sides measure 6 centimeters. The radius of the circle is closest to: a. 75 ft by 2 ft a. 4 centimeters b. 30 ft by 5 ft b. 3 centimeters c. 15 ft by 10 ft c. 5 centimeters d. 50 ft by 3 ft d. 6 centimeters Rhombus ABCD has an area of 264 square units. If DB = 12 units, find AC. a. 44 units c. 18 units b. 22 units d. 12 units 5. 2.3d What is the height of a parallelogram with a base of 9 centimeters and an area of 36 square centimeters? a. 6 centimeters b. 4 centimeters c. 2 centimeters d. 9 centimeters Moore Public Schools Geometry EOI Practice 28 The circumference of the plate shown below is 84.5 cm. To the nearest hundredth, what is the plate’s diameter? Use π = 3.14. a. 5.19 cm c. 13.46 cm b. 10.38 cm d. 26.91 cm Geometry EOI Practice 6. 2.3d 7. 2.3d 8. 2.3d A square with an area of 64 square inches has a perimeter of _?_ 9. 2.3d The circumference of a circle is divided by 2π . What is the result? a. 64 in. c. 32 in. a. r 2 c. 2r b. 16 in. d. 128 in. b. r d. π A triangle has an area of 72 square feet and a height of 9 feet. Find its base. a. 16 ft c. 32 ft b. 8 ft d. 9 ft 10. The center of a circle is located at ( −4, 0 ) . Point ( 0, 0 ) lies on 2.3d the edge of the circle. What is the circumference of the circle? The perimeter of an equilateral triangle is 18. What is the length of each altitude of the triangle? a. 3 3 c. 12 b. 6 d. 6 3 Moore Public Schools Geometry EOI Practice 29 a. 16π c. 8π b. −4π d. 4π Geometry EOI Practice PASS 2.4a: Determine and verify the relationships of similarity of triangles, using algebraic and deductive proofs. 1. Which statement is true about 2.4a the triangles? 3. Which of the following 2.4a statements is true about the triangles below? a. ABC ∼ DEF by AA. b. ABC ∼ DEF by SSS. c. ABC ∼ DEF by SAS. d. The triangles can not be proven similar. a. QRS ∼ TUV by AA. b. QRS ∼ TUV by SSS. c. QRS ∼ TUV by SAS. d. The triangles can not be proven similar. 2. Which triangle is similar to ABC ? 2.4a 4. In QRS , TU RS . Which of 2.4a the following statements is not true by the Side-Splitting Theorem? C a. c. b. d. a. b. Moore Public Schools Geometry EOI Practice 30 QT TR TR QR = QU = US US QS c. d. QT QS QT QU = QU = QR TR US Geometry EOI Practice 5. Use the Side-Splitting 2.4a Theorem to find x. a. 2.5 units b. 6.4 units 8. Find the triangle similar to ABC below. 2.4a a. c. b. d. c. 7 units d. 10 units 6. Using the Side-Splitting 2.4a Theorem, determine x. 9. Which theorem or postulate 2.4a can be used to prove that these two triangles are similar? a. 2 units b. 6 units c. 9 units d. 12 units a. AA b. SAS ABC ∼ DEF . Which of the 7. 2.4a c. SSA d. SSS following is not true? a. b. AB DE AB DE = = EF BC AC DF c. AC BC = 10. Identify the true statement 2.4a for the figure below. DF EF d. ∠B ≅ ∠E a. b. Moore Public Schools Geometry EOI Practice 31 PQR ~ RST PQR ~ TSR c. d. PQR ~ STR PQR ~ TRS Geometry EOI Practice 11. If the corresponding sides of 2.4a two triangles are proportional, then _?_. 13. 2.4a If ABC ~ PBQ, then which of the following proportions is not true? a. the triangles are congruent b. the triangles are right triangles c. corresponding side lengths are equal d. the triangles are similar a. b. PB AB AC PQ = PQ = CB AC QB c. d. AP PB AP PB = = AC PQ CQ QB 12. Shown below is an 2.4a illustration of the _?_. 14. The postulate or theorem 2.4a that can be used to prove that the two triangles are similar is _?_. a. AA Similarity Postulate b. SAS Similarity Theorem c. SSS Similarity Theorem d. SAS Congruence Theorem a. SSS Similarity Theorem b. SAS Similarity Theorem c. AA Similarity Postulate d. ASA Congruence Theorem Moore Public Schools Geometry EOI Practice 32 Geometry EOI Practice PASS 2.4b: Use ratios of similar 2-dimensional figures to determine unknown values, such as angles, side lengths, perimeter or circumference, and area. 1. Which measure is the height 2.4b of the flagpole in the diagram? 3. Triangles ABC and DEF are 2.4b similar. The similarity ratio of ABC to DEF is 5 , 2 AB = 40, BC = 25, and AC = 35. What is the perimeter of DEF ? a. 20 units b. 40 units a. 11.2 feet b. 15 feet c. 17.5 feet d. 20 feet 4. Figure ABCDE is similar to 2. The triangles below are 2.4b c. 60 units d. 100 units 2.4b similar. The area of the figure A ' B ' C ' D ' E '. What is the length of A ' E '? larger triangle is 48 in. 2 . What is the area of the smaller triangle? a. 16 in. 2 b. 12 in. 2 Moore Public Schools Geometry EOI Practice a. 0.72 b. 2.00 c. 8 in. 2 d. 3 in. 2 33 c. 2.40 d. 3.60 Geometry EOI Practice 5. A surveyor wants to find the 2.4b distance d across a river. Using the measurements shown, what is a good estimate of d, in feet? a. 30 feet b. 40 feet 8. Compare the larger circle to 2.4b the smaller circle. Which of the following correctly list the ratios of their circumferences, C, and their areas, A? c. 50 feet d. 60 feet a. C = 6. A person that is 5 feet tall 2.4b casts a 3.5-foot long shadow. At the same time a telephone pole casts a 14-foot shadow. How tall is the telephone pole? c. 17.0 feet d. 20.0 feet 2.4b 7. Find the height, x, of the 2.4b triangle. Moore Public Schools Geometry EOI Practice 28 4 16 7 49 4 16 21 12 Find the b. 34 441 ,A= 7 4 ABC ~ DEF . a. c. 50 d. 60 144 7 c. C = , A = 9. a. 30 b. 40 21 ,A= b. C = , A = d. C = a. 9.8 feet b. 15.5 feet 12 16 9 4 3 area ABC area DEF . c. d. 16 3 4 9 Geometry EOI Practice 10. The ratio of side lengths of ABC to DEF is 3:1. Find the 2.4b lengths of EF and AC. 13. Find x if ABC ~ JKL. 2.4b a. 10 b. 14 a. EF = 3, AC = 3 5 c. 25 d. 29 b. EF = 6, AC = 9 5 c. EF = 6, AC = 3 5 14. If quadrilateral ABCD ~ 2.4b quadrilateral EFGH, find x. d. EF = 6, AC = 21 11. In the diagram, 2.4b AB BD = AC CE . Find the length of AE. a. 15 b. 20 a. 7.5 c. 17.5 b. 15 d. 13 c. 25 d. 30 15. The rectangles below are 2.4b similar. Find the value of s. 1 3 12. The ratio of the perimeters ABC to KLM is 3:5. 2.4b of Which ratio could not be a ratio of two corresponding sides? a. b. 1.5 2.5 6 10 Moore Public Schools Geometry EOI Practice c. 9:15 a. 2.5 b. 3.0 d. 6:15 35 c. 3.5 d. 4.0 Geometry EOI Practice PASS 2.5a: Determine and verify the relationships of congruency of triangles, using algebraic and deductive proofs. 1. Which postulate or theorem 2.5a proves the triangles congruent? 3. Which set of figures 2.5a demonstrates the ASA Postulate? a. b. a. SSS b. ASA c. SAS d. AAS c. 2. Which postulate or theorem 2.5a proves the triangles congruent? d. 4. Which set of figures 2.5a demonstrates the AAS Postulate? a. SAS b. AAS c. SSS d. ASA a. b. c. d. Moore Public Schools Geometry EOI Practice 36 Geometry EOI Practice 5. If CJW ≅ AGS , m∠A = 50, m∠J = 45, 2.5a and m∠S = 16 x + 5, what is x? a. 17.5 b. 11.875 7. What are the congruent 2.5a triangles in the diagram? c. 6 d. 5 a. b. 6. What reason should be given 2.5a for statement 5 in the proof? ABC ≅ EBD ABE ≅ CBD c. d. AEB ≅ CBD ABE ≅ CDB 8. In the figure below, 2.5a AC ≅ DF and ∠A ≅ ∠D. Given: DB is the perpendicular bisector of AC . Prove: ADB ≅ CDB Statements 1. DB is the perpendicular bisector of AC 2. AB ≅ CB 3. ∠ABD ≅ ∠CBD 4. DB ≅ DB 5. ADB ≅ CDB Which additional information would be enough to prove that ABC ≅ DEF ? Reasons a. AB ≅ DE c. BC ≅ EF b. AB ≅ BC d. BC ≅ DE 1. Given 2. Midpoint Theorem 3. ⊥ line; all right ∠ s are ≅ 4.Reflexive Property 5. _?_ a. SSS b. AAS Moore Public Schools Geometry EOI Practice c. ASA d. SAS 37 Geometry EOI Practice 9. In the figure below, it is 2.5a given that BD ≅ CE. To prove BCD ≅ CBE by the SSS Congruence Theorem, what additional information is sufficient? 11. In the figure below, it is 2.5a given that AD ≅ AE. To prove ADC ≅ AEB by the ASA Congruence Theorem, what additional information is sufficient? a. ∠A ≅ ∠A c. AB ≅ AC a. DC ≅ EB c. ∠ADC ≅ ∠AEB b. DC ≅ EB d. ∠ADC ≅ ∠AEB b. AB ≅ AC d. ∠A ≅ ∠A 12. Given ABC ≅ DEF , which 2.5a statement is true? 10. Under the conditions stated 2.5a below, what postulate implies that GHJ and MHO are congruent? OH ≅ JH , ∠O ≅ ∠J a. ∠A ≅ ∠E c. BC ≅ EF b. ∠B ≅ ∠F d. AC ≅ DE 13. In PQR and KLM , 2.5a ∠P ≅ ∠K , PQ ≅ KL, and ∠Q ≅ ∠L. Which side is congruent to RQ ? a. ASA c. SSS b. SAS d. AAS Moore Public Schools Geometry EOI Practice 38 a. KM c. KL b. ML d. cannot be determined Geometry EOI Practice 14. Which theorem or postulate 2.5a can be used to show ABC ≅ CDA ? 15. The angle needed to apply 2.5a the SAS postulate is the a. right angle b. obtuse angle c. acute angle d. included angle a. HL b. SSS Moore Public Schools Geometry EOI Practice c. SAS d. AAS 39 Geometry EOI Practice PASS 2.5b: Use the relationships of congruency of 2-dimensional figures to determine unknown values, such as angles, side lengths, perimeter or circumference, and area. 3. EFGHIJ ≅ KLMNOP. What 2.5b is the length of KL ? 1. Which best describes the 2.5b measure of ∠ABC ? a. 30˚ b. 110.5˚ c. 108˚ d. 74.5˚ 2. Using the congruence 2.5b markings on the figure, what is x? a. 2 b. 5 c. 7 d. 12 4. Given ∠X ≅ ∠A and ∠Z ≅ ∠C , 2.5b find the value of x. a. 6˚ b. 4˚ c. 15˚ d. 9˚ a. 25 b. 27 Moore Public Schools Geometry EOI Practice 40 c. 29 d. 30 Geometry EOI Practice 5. In ABCD, AB ≅ CD and BC ≅ AD. 2.5b What is the value of x? a. 5 c. 7 b. 10 d. 6 7. In the diagram, MN is the 2.5b perpendicular bisector of AD. What are the values of x and y? a. x = 2, y = 7 c. x = 8, y = 11 b. x = 8, y = 2 d. x = 2, y = 8 6. AB ≅ CD. Find the length of 2.5b BD. 8. M is the midpoint of LN . Find 2.5b the value of x. a. 8 c. −4 b. 10 d. 7 a. 19 c. 25 b. 43 d. 50 9. EF bisects ∠DEG. What is 2.5b ∠DEF ? Moore Public Schools Geometry EOI Practice 41 a. 28.5° c. 114° b. 57° d. 29.5° Geometry EOI Practice 10. In the diagram, WX ≅ YZ . 2.5b 13. For what value of x is 2.5b ∠ATK ≅ ∠MJS if m∠ATK = 5 x + 4 and m∠MJS = 8 x − 11? Find the length of XZ. a. 11 c. 15 b. 2 d. 26 a. 29 c. 10 b. 15 d. 5 14. m∠WOX = 2 x + 1 and 2.5b m∠XOY = 3 x − 9. Find m∠WOY . 11. In the diagram, AB ≅ DE and 2.5b BC ≅ CD. Find the length of CE. a. 11 c. 10 b. 22 d. 16 12. In WXYZ, WZ ≅ XY . What is 2.5b the value of x? a. 1.6 c. 12 b. 3 d. 4 Moore Public Schools Geometry EOI Practice 42 a. 10 c. 42 b. 21 d. 52 Geometry EOI Practice PASS 2.6a: Find angle measures and arc measures related to circles. 5. Find m∠1. For Exercises 1-4, use the circle below. 2.6a a. 170˚ b. 85˚ c. 190˚ d. 95˚ 1. Find mBC. 2.6a a. 55˚ b. 90˚ 6. Find m AB. c. 35˚ d. 110˚ 2.6a 2. Find mCD. 2.6a a. 55˚ b. 90˚ c. 35˚ d. 110˚ a. 110˚ b. 70˚ c. 140˚ d. 220˚ 3. Find mCAE. 2.6a a. 180˚ b. 125˚ c. 145˚ d. 215˚ 7. Find m ABC. 2.6a 4. Which statement is not true? 2.6a a. b. c. d. m AC = mCD m AB = mED m AE = mBC + mCD mCD = m AE Moore Public Schools Geometry EOI Practice a. 58˚ b. 244˚ 43 c. 122˚ d. 29˚ Geometry EOI Practice 8. If mEGF = (6 x + 12)° , find the value of x. 9. If mLNM = (8 x + 12)° , find the value of x. 2.6a 2.6a a. 22 b. 11 Moore Public Schools Geometry EOI Practice c. 16 d. 10 a. 14 b. 16.8 44 c. 28 d. 29 Geometry EOI Practice PASS 2.6b: Find angle measures and segment lengths using the relationships among radii, chords, secants, and tangents of a circle. 1. Use the diagram to find the 2.6b value of x. Round to the nearest hundredth, if necessary. 4. If an inscribed angle has a 2.6b measure of 100˚, what is the measure of the intercepted arc? a. 100˚ b. 200˚ a. 4 b. 5 c. 50˚ d. 0˚ c. 5.62 d. 5.83 5. Find the value of x. 2.6b 2. Use the diagram to find the 2.6b value of x. a. 178 b. 356 a. 10 b. 20 c. 22 d. 11 c. 89 d. 182 6. If mLNM = 280°, find the value 2.6b of y. 3. What is m AB ? 2.6b a. 40 b. 80 a. 10˚ b. 20˚ Moore Public Schools Geometry EOI Practice c. 30˚ d. 40˚ 45 c. 160 d. 140 Geometry EOI Practice 7. Find the values of a and b. 10. Find the values of x and y. 2.6b 2.6b a. a = 50, b = 50 b. a = 25, b = 50 c. a = 50, b = 25 d. a = 25, b = 25 a. b. c. d. 8. Find the value of x. x = 6, y = 84 x = 42, y = 48 x = 42, y = 42 x = 48, y = 42 2.6b 11. Find m∠1 . 2.6b a. 5 b. 3 c. 8 d. 10 a. 75˚ b. 190˚ c. 95˚ d. 150˚ 9. Find the values of x and y. 2.6b 12. Find m∠1 . 2.6b a. x = 80, y = 75 b. x = 105, y = 100 c. x = 75, y = 80 a. 64˚ b. 32˚ d. x = 100, y = 105 Moore Public Schools Geometry EOI Practice 46 c. 108˚ d. 54˚ Geometry EOI Practice 13. Find the value of y. 16. Find the value of x. 2.6b 2.6b a. 10 b. 5 a. 26 b. 77 c. 102 d. 51 17. You are standing 16 feet 2.6b from a circular swimming pool. The distance from you to a point of tangency is 25 feet. What is the approximate diameter of the pool? 14. Find the value of x. 2.6b a. 3 b. 4 a. 23 ft b. 46 ft c. 5 d. 6 15. Find the value of y. 2.6b a. 2 b. 3 Moore Public Schools Geometry EOI Practice c. 9.6 d. 14 c. 4 d. 5 47 c. 19 ft d. 38 ft Geometry EOI Practice PASS 3.1: Use the Pythagorean Theorem and its converse to find missing side lengths and to determine acute, right and obtuse triangles, and verify using algebraic and deductive proofs. 4. What is the length of the 3.1 hypotenuse of the triangle below to the nearest tenth? 1. Find the missing length. 3.1 a. 13.23 c. 35 b. 25 d. 625 2. What is the perimeter of 3.1 the nearest tenth? ABC to a. 19.8 in. c. b. 22.2 in. d. 20.2 in. b. acute d. right Moore Public Schools Geometry EOI Practice b. 8.6 in. d. 7.6 in. a. 11 ft c. 13 ft b. 12 ft d. 14 ft 6. What is the perimeter of 3.1 the nearest tenth? 3. If a triangle has sides of 15, 9, and 3.1 20, is it an obtuse, acute, equilateral, or right triangle? c. equilateral c. 8.1 in. 5. A farmer leans a 12-ft ladder 3.1 against a barn. The base of the ladder is 3 ft from the barn. To the nearest foot, how high on the barn does the ladder reach? 9.9 in. a. obtuse a. 9.1 in. 48 ABC to a. 19.8 in. c. 9.9 in. b. 22.2 in. d. 20.2 in. Geometry EOI Practice 7. What is the perimeter of the figure 3.1 below? 9. A triangle with side lengths of 5, 3.1 12, and 13 is a(an): a. acute triangle b. right triangle c. obtuse triangle a. 52 units c. 47.8 units b. 30 units d. 49.5 units d. straight triangle 10. What is the perimeter of the triangle below? Round the 3.1 answer to the nearest tenth of a unit. 8. If ABCD is a square and BC = 4 3.1 kilometers, what is BD? a. 4 2 kilometers b. 4 kilometers c. 4 3 kilometers d. 8 kilometers a. 9.3 units b. 12.0 units c. 20.6 units d. 86.0 units Moore Public Schools Geometry EOI Practice 49 Geometry EOI Practice PASS 3.2: Apply the 45-45-90 and 30-60-90 right triangle relationships to solve problems, and verify using algebraic and deductive proofs. 1. Find the value of x. 4. In 3.2 3.2 a. 24 2 c. 12 2 b. 24 d. 12 2. Find the values of x and y. ABC , what is BC? a. 4 3 c. 8 b. 4 d. 8 2 5. A triangle whose side lengths 3.2 measure 3, 3, and 3 2 is often referred to as a(an): 3.2 a. 45-45-90 triangle b. 30-60-90 triangle a. x = 15 3; y = 45 c. obtuse triangle b. x = 15 2; y = 30 d. acute triangle c. x = 30; y = 45 d. x = 15 3; y = 30 6. What is the length of the 3.2 hypotenuse of a triangle with vertices of (5, 5), (5, − 4), and ( − 4, − 4)? 3. What is AC? 3.2 a. 5 2 c. 10 2 b. 20 d. 5 3 Moore Public Schools Geometry EOI Practice 50 a. 18 2 c. 9 2 b. 9 3 d. 81 2 Geometry EOI Practice 7. In order to determine the area 3.2 of a trapezoid, you must know the height. What is the height of the trapezoid shown? a. 3 b. 5 2 2 c. 5 d. 5 2 8. Find the perimeter of the 3.2 parallelogram. Leave your answer in simplest radical form. a. 13 + 5 2 units b. 26 + 5 2 units c. 26 + 10 2 units d. 26 + 25 2 units Moore Public Schools Geometry EOI Practice 51 Geometry EOI Practice PASS 3.3: Express the trigonometric functions as ratios and use sine, cosine, and tangent ratios to solve real-world problems. 3. Find x to the nearest hundedth. 1. Choose the correct expression for tan H. 3.3 3.3 a. x = 24.89 a. b. 2. In 3.3 GK KH GH KH c. d. b. x = 13.43 GK GH c. x = 10.28 KH d. x = 12.26 KG 4. From a point 125 feet from the 3.3 base of a building, the angle of elevation from the ground to the top of the building is 50°. STU , what is the sine ratio of ∠T ? a. b. 9 15 12 15 c. d. 9 12 What is the height (h) of the building? Round the answer to the nearest foot. 15 12 a. 105 feet b. 149 feet c. 163 feet d. 194 feet Moore Public Schools Geometry EOI Practice 52 Geometry EOI Practice 5. Using the dimensions of the sail 3.3 given, which most closely represents sin A? 7. A ship’s anchor rests on the sea 3.3 floor 125 feet below the surface. The angle of elevation from the anchor to the ship is 38°. How long is the anchor chain to the nearest foot? a. 77 feet c. 160 feet b. 159 feet d. 203 feet 8. At a certain time, a vertical pole 10 feet tall casts a 14-foot shadow. What is the angle of elevation of the sun to the nearest degree? 3.3 a. 0.4706 c. 1.1333 b. 0.8824 d. 1.8750 6. Johnny wants to build a 15-foot 3.3 sloped roof at an angle of 43°, as shown in the diagram below. What is the height (h) of the beam that is needed to support the roof? Round the answer to the nearest foot. a. 10 feet c. 14 feet b. 11 feet d. 22 feet Moore Public Schools Geometry EOI Practice 53 a. 36° c. 46° b. 44° d. 54° Geometry EOI Practice PASS 4.1a: Identify, describe, and analyze polyhedra (for example, regular, decahedral). 1. Which of the figures shown is not 4.1a a polyhedron? a. I only c. III only b. II only d. II and III 4. Use Euler’s Theorem to find the 4.1a number of faces when a polyhedron has 8 vertices and 12 edges. a. 4 c. 8 b. 6 d. 10 5. Which is the best description of 4.1a the cross section of the figure shown? 2. The polyhedron below has how 4.1a many faces (F) and edges (E)? a. F = 6, E = 18 b. F = 6, E = 24 c. F = 8, E = 18 d. F = 8, E = 24 3. The polyhedron below has how 4.1a many vertices? a. 14 c. 16 b. 15 d. 17 Moore Public Schools Geometry EOI Practice 54 a. circle c. rectangle b. square d. oval Geometry EOI Practice PASS 4.1b: Use properties of 3-dimensional figures; side lengths, perimeter or circumference, and area of a face; and volume, lateral area, and surface area to determine unknown values and correctly identify the appropriate unit of measure of each. 3. Find the surface area of the regular 4.1b right prism. 1. The best mathematical name of the 4.1b solid is a. right prism. a. 215 in.² c. 105 in.² b. right rectangular prism. b. 160 in.² d. 187.5 in.² c. cube. 4. Find the surface area of a right 4.1b rectangular prism with a height of 6 inches, a length of 2 inches, and a width of 8 inches. d. right pentagonal prism. 2. Find the lateral area of the right prism shown. 4.1b a. 96 in.² c. 152 in.² b. 120 in.² d. 128 in.² 5. Find the surface area of the right 4.1b cylinder. Round to the nearest hundredth. a. 105 m 2 c. 85 m 2 b. 90 m2 d. 74 m2 Moore Public Schools Geometry EOI Practice 55 a. 831.27 in.² c. 395.84 in.² b. 252 in.² d. 506.68 in.² Geometry EOI Practice 6. Use the diagram to solve for the 4.1b value of x given that the surface area of the figure is 286 in.². a. 14 in. c. 6 in. b. 12 in. d. 7 in. 9. Find the surface area of the cone. 4.1b Round to the nearest tenth. a. 317.0 m² c. 239.4 m² b. 241.7 m² d. 278.2 m² 10. Use the diagram to solve for x 4.1b and y when the surface area is 138.23 m². 7. Find the slant height of the 4.1b pyramid. a. 4.5 cm c. 6.5 cm a. x = 9.8 m, y = 10 m b. 5.5 cm d. 6 cm b. x = 11 m, y = 10.8 m c. x = 8 m, y = 7.7 m 8. Find the slant height of the cone. 4.1b Round to the nearest tenth. d. x = 20 m, y = 19.9 m 11. Find the surface area of the solid. 4.1b The cylinder and cones are right. Round to the nearest tenth. a. 716.3 m² b. 867.1 m² a. 20.0 c. 8.9 b. 10.6 d. 14.4 Moore Public Schools Geometry EOI Practice c. 1168.7 m² d. 942.5 m² 56 Geometry EOI Practice 12. Find the lateral area of the 4.1b pyramid. 16. Find the volume of a prism that 4.1b has a height of 10.5 m and has a right triangle for a base. The legs of the triangle are 5 m and 7 m. Round answer to nearest hundredth. a. 57.5 cm² b. 65 cm² c. 32.5 cm² d. 78 cm² 13. What is the volume of a prism with a rectangular base, with 4.1b sides of 5 feet and 6 feet, and a height of 4 feet? a. 183.75 m 3 c. 367.5 m 3 b. 225.80 m 3 d. 316.14 m 3 17. A cylinder has a radius of 24.6 3 4.1b in. and a volume of 29,468 in. . Find its height. a. 60 ft 3 c. 120 ft 3 a. 14.5 in. c. 15 in. b. 240 ft 3 d. 180 ft 3 b. 15.5 in. d. 16 in. 18. Find the value of x if the volume of the prism is 105 cm 3 . 4.1b 14. Find the value of x if the right 3 4.1b prism has a volume of 24 m . a. 1 m a. 2 cm b. 2 m b. 3 cm c. 3 m c. 4 cm d. 4 m d. 5 cm 19. Find the surface area of the 4.1b sphere. Round to the nearest tenth. 15. Find the volume of the right 4.1b cylinder. Round the answer to the nearest hundredth. a. 324.59 ft 3 a. 175.9 in.² b. 216.97 ft 3 b. 615.8 in.² c. 1996.22 ft 3 c. 307.8 in.² d. 681.64 ft 3 d. 461.8 in.² Moore Public Schools Geometry EOI Practice 57 Geometry EOI Practice 20. Find the volume of the sphere. 4.1b Round to the nearest tenth. a. 44,602.2 m 3 b. 1520.5 m 3 c. 1393.8 m 3 d. 5575.3 m 3 21. What is the radius of a sphere 4.1b with surface area of 1963.5 cm²? a. 11 cm c. 11.5 cm b. 12.5 cm d. 12 cm 22. Find the circumference of the great circle if the volume of the 4.1b sphere is 179.6 m 3 . Round to the nearest tenth. a. 22 m c. 11 m b. 23.8 m d. 11.9 m 23. Find the surface area of the 4.1b hemisphere. Round to the nearest tenth. a. 706.9 cm² b. 1413.7 cm² c. 2120.6 cm² d. 3534.3 cm² Moore Public Schools Geometry EOI Practice 58 Geometry EOI Practice PASS 4.2a: Use ratios of similar 3-dimensional figures to determine unknown values such as angles, side lengths, perimeter or circumference of a face, area of a face, and volume. 4. Which of the following describes 4.2a the two spheres? 1. Two prisms are similar with a 4.2a scale factor of 1:4. Find the volume of the first given that the volume of the second is 2400 ft 3 . a. 600 ft 3 c. 150 ft 3 b. 37.5 ft 3 d. 75 ft 3 c. 1024 m3 b. 640 m3 d. 97.7 m3 c. both A and B b. similar d. neither A nor B 5. Two similar prisms have equilateral 4.2a triangular bases and the edges of the bases are 50 centimeters and 20 centimeters. Find the ratio of the perimeters of the bases. 2. Two pyramids are similar with a 4.2a ratio of surface areas of 25:64. Find the volume of the second pyramid given that the first has a volume of 250 m3 . a. 61.0 m3 a. congruent a. 5 2 : 2 5 c. 25:4 b. 5:2 d. 125:8 6. Two square pyramids are similar. 4.2a The sides of the bases are 4 inches and 12 inches. The height of the smaller pyramid is 6 inches. Find the height of the larger pyramid. 3. Which solid is similar to this 4.2a solid? a. 24 in. c. 16 in. b. 18 in. d. 14 in. 7. The ratio of the radii of two similar 4.2a cylinders is 3:5. The volume of the smaller cylinder is 54π cubic centimeters. Find the volume of the larger cylinder. Moore Public Schools Geometry EOI Practice 59 a. 90π cm3 c. 250π cm3 b. 150π cm3 d. 540π cm3 Geometry EOI Practice PASS 4.2b: Use the relationships of congruency of 3-dimensional figures to determine unknown values, such as angles, side lengths, perimeter or circumference of a face, area of a face, and volume. 3. Cylinders A and B are congruent. 4.2b Cylinder A has a height of 3 inches and a lateral area of 30π square inches. What is the surface area of cylinder B? 1. Two solids are congruent. Which 4.2b statement about the two solids is true? a. They have a scale factor of 1. LA = 2π rh b. Their corresponding angles are congruent. SA = 2π r 2 + 2π rh c. The ratio of the corresponding linear measurements is 1:1. a. 30π square inches b. 50π square inches d. All of the above are true statements. c. 55π square inches d. 80π square inches 2. Samantha is making pincushions 4.2b that are congruent rectangular prisms. The volume of one pincushion is 96 cubic centimeters, the height is 2 centimeters, and the length is 6 centimeters. What is the width of the other pincushion? a. 2 centimeters b. 4 centimeters c. 6 centimeters d. 8 centimeters Moore Public Schools Geometry EOI Practice 60 Geometry EOI Practice PASS 4.3: Create a model of a 3-dimensional figure from a 2-dimensional drawing and make a 2-dimensional representation of a 3-dimensional object (for example, nets, blueprints, perspective drawings). 1. Which net represents the surfaces 4.3 of a square pyramid? a. b. c. d. 2. Which of the following patterns 4.3 could not be folded into a cube? . . a. . b. . c. . d. . . . Moore Public Schools Geometry EOI Practice 61 Geometry EOI Practice 3. Which could be the view of this 4.3 stack of cubes from directly above? a. b. c. d. 4. Which represents a two4.3 dimensional view from directly above the figure? . a. . b. . c. . d. . . . 5. Below are the front, side, and top 4.3 views of a building. . How tall (in stories) is the building? Moore Public Schools Geometry EOI Practice 62 a. 1 c. 3 b. 2 d. 4 Geometry EOI Practice 6. What figure does the net 4.3 represent? 8. Which is the top view of the farm 4.3 buildings shown above? a. a right triangular prism b. a right cylinder c. a regular cube a. . b. . d. a regular triangular pyramid 7. Below are the front, side, and top 4.3 views of a building. c. Where is the tallest part of the building located? d. a. front left section b. back right section c. back left section d. front right section Moore Public Schools Geometry EOI Practice 63 .. ;. Geometry EOI Practice PASS 5.1: Use coordinate geometry to find the distance between two points; the midpoint of a segment; and to calculate the slopes of parallel, perpendicular, horizontal, and vertical lines. 3. If (2, 2), (8, 2), (8, 8), and (2, 8) 5.1 are the vertices of a square, what are the slopes of its diagonals? 1. Which equation best 5.1 represents a line parallel to t? a. 1 and 1 c. 1 and -1 b. 0 and undefined d. 0 and 0 4. DE has endpoints (-3, 4) and (5, 2). What is the midpoint of DE ? 5.1 a. y = −2 c. x = 2 b. y = x − 2 d. x = −2 a. (1, 1) c. (2, 2) b. (4, 3) d. (1, 3) The grid below shows the location of a high school and a library. A community center is at the midpoint between the school and the library. 2. Which equation best 5.1 represents a line parallel to t? a. y = 2 x − 2 1 b. y = 1 x + 2 2 Moore Public Schools Geometry EOI Practice 5. What are the coordinates of the 5.1 community center? c. y = − x − 2 d. y = − x + 2 64 a. (2, 2) c. (4, 2) b. (2, 4) d. (4, 4) Geometry EOI Practice 7. Tim made a graph of the location of 5.1 some playground equipment as shown above. What is the distance between the swings and the slide to the nearest tenth of a unit? 6. The figure above shows the location 5.1 of two flags on the city’s courthouse grounds. The state flag will be located at the midpoint between the U.S. flag and the city flag. At which point will the state flag be located? a. 7.1 ⎛ 11 5 ⎞ a. ⎜ − , ⎟ ⎝ 2 2⎠ b. 7.6 b. ( −3, 5 ) c. 12.7 ( −1, 2 ) d. 13.0 c. ⎛3 1⎞ d. ⎜ , − ⎟ ⎝2 2⎠ Moore Public Schools Geometry EOI Practice 65 Geometry EOI Practice 9. The line in the diagram above 5.1 represents a cable used to support a newly planted tree. A second cable is needed that is parallel to the existing cable. Which could be the equation of a second cable? a. y = −2 x + 5 8. What is the midpoint of AB shown 5.1 on the graph above? 1 b. y = − x + 5 2 ⎛ 9 ⎞ a. ⎜ − , 3 ⎟ ⎝ 2 ⎠ c. y = d. y = 2 x + 5 ⎛3 ⎞ b. ⎜ , 1⎟ ⎝2 ⎠ c. 1 x+5 2 ( 3, 2 ) 10. Find the slope of the line through 5.1 ( −5, − 1) and ( −2, − 1) . ⎛9 ⎞ d. ⎜ , − 3 ⎟ ⎝2 ⎠ a. 0 c. 3 4 b. undefined d. 4 3 11. The slope of a line perpendicular to the line whose equation is 5.1 y = 3 x − 4 is Moore Public Schools Geometry EOI Practice 66 a. − 1 3 c. −3 b. 1 3 d. −1 Geometry EOI Practice 12. Find the distance between points 5.1 P (1, − 2 ) and Q ( 0, 2 ) . a. 15 c. 13 b. 17 d. 5 13. Find the coordinates of the other endpoint of a segment with an 5.1 endpoint of X (13, 5 ) and midpoint M ( 8, 3) . a. (18, 7 ) c. ( 3, 7 ) b. (18, 1) d. ( 3, 1) 14. Find the coordinates of the other endpoint of a segment with an 5.1 endpoint of X ( −2, 3) and midpoint M (1, − 2 ) . a. ( 4, − 7 ) b. ( −4, 7 ) Moore Public Schools Geometry EOI Practice c. ( 0, − 1) d. ( −5, 8) 67 Geometry EOI Practice PASS 5.2a: Given a set of points determine the type of figure formed based on its properties. 1. What is the classification of ABC 5.2a with vertices A(4,1), B(2, -1), and C(-2, -1) by its sides? a. equilateral c. scalene b. isosceles d. right 2. What is the classification of ABC 5.2a with vertices A(0, 0), B(4, 3), and C(4, -3) by its sides? a. equilateral c. scalene b. isosceles d. right 3. ABCD is a parallelogram with 5.2a A(0, 0), B(2, 4), and C(10, 4). Find the possible coordinates of D. a. (8, 0) c. (0, 4) b. (10, 0) d. (10, 8) 4. What is the most precise name for a 5.2a quadrilateral with (2, -1), (6, 3), (-2, 3), and (2, 9)? a. rectangle c. kite b. parallelogram d. rhombus 5. What special type of quadrilateral 5.2a has the vertices F(-6, -2), G(1, -2), H(-6, -5), and I(1, -5)? a. rectangle c. square b. parallelogram d. rhombus Moore Public Schools Geometry EOI Practice 68 Geometry EOI Practice PASS 5.2b: Use transformations (reflection, rotation, translation) on geometric figures to solve problems within coordinate geometry. 1. Choose the notation below that 5.2b describes the translation. 3. The coordinates of JKL are 5.2b J(-1, 2), K(-2, -1), and L(2, 1). The component form of MN is 3, − 4 . What are the coordinates of J ′K ′L′ after the translation using MN ? a. J ′(−4, − 2), K ′(1, − 3), L′(5, − 5) b. J ′(2, − 2), K ′(1, − 3), L′(5, − 3) a. ( x, y ) → ( x − 3, y + 4) c. J ′(2, − 2), K ′(1, − 3), L′(5, − 5) b. ( x, y ) → ( x − 3, y − 4) d. J ′(2, − 2), K ′(1, − 5), L′(5, − 3) c. ( x, y ) → ( x − 4, y + 3) d. ( x, y ) → ( x − 4, y − 3) A windmill has eight equally spaced blades that rotate in the clockwise direction. 2. Choose the correct name and 5.2b component form of the vector shown. a. JH , 3,4 b. JH , −3, −4 c. JH , −4, −3 4. How many degrees must blade P 5.2b rotate to reach the location of blade U? d. HJ , 3,4 Moore Public Schools Geometry EOI Practice 69 a. 45° c. 225° b. 135° d. 300° Geometry EOI Practice 5. To plan a scene in an animated 5.2b movie, Roger rotates the above figure around point P by 90° in a clockwise direction. Which drawing shows the pre-image and the final image? 6. Which would move Flag A to Flag B 5.2b in the grpah above? a. a. clockwise rotation of 180° b. reflection over x-axis, then clockwise rotation of 90° c. translation 8 units left and 7 units down b. d. reflection over y-axis, then translation 8 units left and 7 units down c. d. Moore Public Schools Geometry EOI Practice 70 Geometry EOI Practice 7. A quilt design is formed by 5.2b translating a polygon across the coordinate plane as shown in the figure above. Which is a translational rule that will translate point A to point B? 9. Janelle and Franz are playing a 5.2b game. The rule of the game is each playing piece must go through one transformation. Janelle reflects piece X over line 3. Where will piece X land? a. ( x, y ) → ( x + 0, y + 8) a. on piece A c. on piece C b. ( x, y ) → ( x − 4, y + 2) b. on piece B d. on piece D c. ( x, y ) → ( x + 2, y + 3) d. ( x, y ) → ( x + 4, y − 2) 10. If the point (2, -5) is reflected in the line y = x, then the image is 5.2b 8. After this translation 5.2b ( x, y ) → ( x + 3, y − 2 ) of point T, what are the coordinates of the new point? a. ( −1, 3) b. ( 0, 4 ) Moore Public Schools Geometry EOI Practice a. (-5, 2) c. (-2, 5) b. (5, -2) d. (-5, -2) 11. What is the image of (-3, 6) when reflected in the x-axis? 5.2b c. ( 3, − 2 ) d. ( 5, − 1) 71 a. (-3, -6) c. (3, -6) b. (-3, 6) d. (3, 6) Geometry EOI Practice Answer Key Pass 1.1 Pass 1.2 Pass 2.2a Pass 2.2b 1. d 1. a 1. a 1. d 2. c 2. d 2. b 2. a 3. c 3. c 3. c 3. c 4. d 4. b 4. b 4. b 5. c 5. d 5. c 5. d 6. a 6. a 6. c 6. b 7. c 7. c 7. d 7. d 8. c 8. d 8. b 8. d 9. c 9. c 9. b 9. d 10. b 10. a 10. b 10. d 11. d 11. c 11. d 12. a 12. a 13. c 13. b 14. b Moore Public Schools Geometry EOI Practice 72 Geometry EOI Practice Pass2.2c 1. b 2. d 1. d 1. d 1. d 3. d 2. c 2. d 2. c 4. d 3. d 3. c 3. b 5. c 4. c 4. b 4. d 6. b 5. c 5. a 5. a 7. b 6. c 6. a 6. c 8. c 7. a 7. d 7. b 9. c 8. a 8. a 8. c 10. d 9. c 9. d 9. a 11. d 10. d 10. a 10. b 12. c 11. b 11. c 11. b 13. a 12. b 12. d 12. a 14. b 13. a 13. c 13. c 15. c 14. b 14. b 14. b 16. a 15. c 15. d 15. c 17. d 16. a 16. a 18. c 17. b 17. c 19. a 18. c 18. a 19. b 19. d 20. c 20. d 21. b 21. c 22. a 22. c 23. d 23. b 24. a 24. a 25. c 26. a 27. d Moore Public Schools Geometry EOI Practice Pass 2.3a Pass 2.3b 73 Pass 2.3c Geometry EOI Practice Pass 2.3d Pass 2.4a Pass 2.4b Pass 2.5a 1. c 1. c 1. c 1. d 2. a 2. b 2. d 2. b 3. b 3. a 3. b 3. b 4. b 4. c 4. b 4. a 5. d 5. d 5. b 5. d 6. c 6. b 6. d 6. d 7. a 7. c 7. a 7. b 8. a 8. b 8. c 8. a 9. b 9. a 9. a 9. b 10. c 10. c 10. b 10. a 11. d 11. c 11. c 12. b 12. d 12. c 13. c 13. d 13. b 14. c 14. c 14. a 15. d 15. d Moore Public Schools Geometry EOI Practice 74 Geometry EOI Practice Pass 2.5b Pass 2.6a Pass 2.6b Pass 3.1 1. b 1. c 1. d 1. b 2. a 2. b 2. c 2. b 3. c 3. d 3. d 3. a 4. c 4. d 4. b 4. d 5. b 5. b 5. c 5. b 6. a 6. c 6. a 6. b 7. d 7. b 7. c 7. c 8. c 8. a 8. d 8. a 9. a 9. d 9. b 9. b 10. d 10. d 10. c 11. d 11. c 12. d 12. b 13. d 13. d 14. c 14. a 15. b 16. d 17. a Moore Public Schools Geometry EOI Practice 75 Geometry EOI Practice Pass 3.2 Pass 3.3 Pass 4.1a Pass 4.1b 1. c 1. a 1. d 1. d 2. d 2. b 2. c 2. b 3. a 3. c 3. c 3. a 4. b 4. b 4. b 4. c 5. a 5. b 5. c 5. d 6. c 6. a 6. d 7. b 7. d 7. c 8. c 8. a 8. d 9. a 10. d 11. d 12. b 13. c 14. d 15. b 16. a 17. b 18. b 19. d 20. a 21. b 22. a 23. a Moore Public Schools Geometry EOI Practice 76 Geometry EOI Practice Pass 4.2a Pass 4.2b Pass 4.3 Pass 5.1 1. b 1. d 1. b 1. a 2. c 2. d 2. d 2. b 3. d 3. d 3. c 3. c 4. b 4. b 4. d 5. b 5. b 5. d 6. b 6. d 6. c 7. c 7. c 7. d 8. b 8. b 9. c 10. a 11. a 12. b 13. d 14. a Moore Public Schools Geometry EOI Practice 77 Geometry EOI Practice Pass 5.2a Pass 5.2b 1. c 1. d 2. b 2. b 3. a 3. d 4. c 4. c 5. a 5. c 6. a 7. d 8. d 9. b 10. a 11. a Moore Public Schools Geometry EOI Practice 78