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1 ABC 2 ABC 3 ABC 4 ABC 5 ABC 6 ABC 7 ABC 8 ABC 9 ABC 10 ABC 11 ABC 12 ABC 13 ABC 14 ABC 15 ABC 16 ABC 17 ABC 18 ABC 19 ABC 20 ABC 21 ABC 22 ABC 23 ABC 24 ABC 25 ABC 26 ABC 27 ABC 28 ABC 29 ABC 30 ABC 31 ABC 32 ABC 33 ABC 34 ABC 35 ABC 36 ABC 37 ABC 38 ABC 39 ABC 40 ABC 41 ABC 42 ABC 43 ABC 44 ABC 45 ABC 46 ABC 47 ABC 48 ABC 49 ABC 50 ABC 51 ABC 52 ABC 53 ABC 54 ABC 55 ABC 56 ABC 57 ABC 58 ABC 59 ABC 60 ABC 61 ABC 62 ABC 63 ABC 64 ABC 65 ABC 66 ABC 67 ABC 68 ABC 69 ABC 70 ABC 71 ABC 72 ABC 73 ABC Geometry 1A Use the figure to name a line containing point A. Any one of these. 1B How many planes are shown in the figure? 6 1C Name three points that are collinear. B, K, A or C, J, B 2A Find the distance between (5, 1) and (-3, -3). 80 4 5 8.9 2B Find the distance between (7, 11) and (-1, 5). 10 2C Find the distance between (2, 0) and (8, 6). 72 6 2 8.5 3A =M(2.5, 1.5) 3B (-6, -4) 3C D 4A Name all angles that have W as a vertex. 4B Name the sides of angle one. 4C Measure angle PMQ and classify it as right, acute, or obtuse. 30˚ acute 5A Name two obtuse vertical angles. angle VZX and angle YZW 5B Name two acute adjacent angles. angle VZY and angle YZT or angle YZT and angle TZW or angle TZW and angle WZX 5C Find the measures of two complementary angles if the difference in the measures of the two angles is 12. 39 & 51 6A Make a conjecture about the next item in the sequence. 6, 8, -32, -30, 120 122 6B Make a conjecture based on the given information. Draw a figure to illustrate your conjecture. Lines l and m are perpendicular. Lines l and m form four right angles 6C Determine whether the conjecture is true or false. Give a counterexample if it is false. Given: JK=KL=LM=MJ Conjecture: JKLM forms a square false 7A Use the following statements to write a compound statement for the disjunction. Then find its truth value. p: An isosceles triangle has two congruent sides. q: A right angle measures 90˚ p or q An isosceles triangle has two congruent sides or a right angle measures 90˚. True. 7B Use the following statements to write a compound statement for the disjunction. Then find its truth value. p: An isosceles triangle has two congruent sides. r: Four points are always coplanar. p and q An isosceles triangle has two congruent sides and four points are always coplanar. True. 7C Use the following statements to write a compound statement for the disjunction. Then find its truth value. p: An acute triangle has two congruent sides. q: An obtuse angle measures 90˚ p or q An acute triangle has two congruent sides or an obtuse angle measures 90˚. False. 8A Write the converse of the conditional statement. Determine whether the converse is true or false. If it is false, find a counterexample. If you have a dog, then you are a pet owner. If you are a pet owner, then you have a dog. False; you could own a hamster. 8B Write the converse of the conditional statement. Determine whether the converse is true or false. If it is false, find a counterexample. If two angles from a linear pair, then they are supplementary. If two angles are supplementary, then they form a linear pair. False. 8C Write the converse of the conditional statement. Determine whether the converse is true or false. If it is false, find a counterexample. If a polygon is a quadrilateral, then the polygon is a rectangle. If a polygon is a rectangle, then it is a quadrilateral. True 9A Write the statement in if-then form. A 32-ounce pitcher holds a quart of liquid. If a pitcher is a 32ounce pitcher, then it holds a quart of liquid. 9B Write the contrapositive of the conditional statement. Determine whether the contrapositive is true of false. If it is false, find a counterexample. If you are 16 years old, then you are a teenager. If you are not a teenager, then you are not 16 years old. True. 9C Write the inverse of the conditional statement. Determine whether the contrapositive is true of false. If it is false, find a counterexample. If you are 16 years old, then you are a teenager. If you not are 16 years old, then you are not a teenager. False. You could be 15. 10A Write the biconditional statement as a conditional and its converse. If false give a counterexample. A triangle is equilateral iff it has three congruent sides. If a triangle is equilateral then it has three congruent sides. True If a triangle has three congruent sides then it is equilateral. True 10B Write the biconditional statement as a conditional and its converse. If false give a counterexample. Two angles are congruent iff they have the same measure. If two angles are congruent, then they have the same measure. True If two angles have the same measure, then they are congruent. True 10C Write the biconditional statement as a conditional and its converse. If false give a counterexample. Two angles are vertical angles if and only if they are congruent. If two angles are vertical angles, then they are congruent. True. If two angles are congruent then they are vertical angles. False. 11A valid 11B invalid 11C Determine whether the stated conclusion is valid based on the given information. If not, write invalid. If three points are noncollinear, then they determine a plane. valid 12A Determine whether statement (3) follows from statements (1) and (2) by the law of Detachment of the Law of Syllogism. If it does, state which law was used. If it does not, write invalid. (1)She is a girl. (2) Her name is Chris. (3)Chris is a girl’s name. Invalid Statement 3 does not follow from statement 2. 12B Determine whether statement (3) follows from statements (1) and (2) by the law of Detachment of the Law of Syllogism. If it does, state which law was used. If it does not, write invalid. (1) Vertical angles are congruent. (2) If two angels are congruent, then their measures are equal. (3) If two angles are vertical, then their measures are equal. Law of Syllogism 12C Determine whether statement (3) follows from statements (1) and (2) by the law of Detachment of the Law of Syllogism. If it does, state which law was used. If it does not, write invalid. ( 1) If Molly arrives at school at 7:30 AM, she will get help in math. (2) If Molly gets help in math, then she will pass her math test. (3) If Molly arrives at school at 7:30 AM, then she will pass her math test. Law of Syllogism 13A Determine whether the statement is always, sometimes, or never true. Explain. If points A, B, and C lie in plane M, then they are collinear. Sometimes; A, B, and C do not necessarily have the be collinear to lie in plane M. 13B B, D, and W are collinear definition of collinear 13C R and W are collinear. Through any two points there is exactly one line. 14A a. 5 – 2/3x = 1 b. Multiplication property c. Distributive property d. -2x = - 12 e. Division property 14B Complete the proof. a. Given d. Subtraction property b. 2(3x+5)/2=7(2) e. x=3 c. substitution 14C Complete the proof. a. 2x-7=1/3x-2 d. 5x-21= -6 b. 3(2x-7)=3(1/3x-2) e. Addition property c. Distributive property f. x=3 15A Complete the proof. 1. Given 2. MN = PQ, PQ = RS 3. Transitive Property 4. Definition of congruent segments. 15B Complete the proof. Given: PQ = RS Prove: PR = QS a. PQ = RS b. PQ + QR = QR + RS c. Segment Addition Postulate d. PR = QS d. substitution 15C Supply the reasons to complete the proof. 1. Given 4. Transitive Property 2. Transitive Property 5. Symmetric Property 3. Given 16A Find the measures of angles A, B, and C. 16B Find the measure of angle 15 and angle 16. angle 15 = 58˚ angle 16 = 58˚ 16C The measures of two complementary angles are in the ratio 4:1. What is the measure of the smaller angle? 18˚ 17A Name all segments that are parallel to 17B Name all segments that intersect 17C Name all segments that are skew to 18A 110˚ 18B x = 30 18C Find the measure of angle LJM. 117˚ 19A Determine whether line AB and line CD are parallel, perpendicular, or neither. A (-2, -5), B (4, 7) C (0, 2), D (8, -2) m line AB = 2 m line CD = -½ (2)(-½) = -1 They are perpendicular. 19B Determine whether line AB and line CD are parallel, perpendicular, or neither. A (-8, -7), B (4, -4) C (-2, -5), D (1, 7) m line AB = 1/4 m line CD = 4 (1/4)(4) ≠ -1 They are not perpendicular or parallel. 19C Determine whether line AB and line CD are parallel, perpendicular, or neither. A (-4, 0), B (0, 3) C (-4, -3), D (8, 6) m line AB = 3/4 m line CD = 3/4 They are parallel. 20A 9 20B Complete the proof. 1. Given 2. Definition of perpendicular 3. All right angles are congruent. 4. If corresponding angles are congruent, the lines are parallel. 20C If 16 3 determine which lines, if any, are parallel. Sate the postulate or theorem that justifies your answer. l ║m corresponding angles 21A If f(x) = x 2 then find 2 f(3a ) = + 2x – 14, 2 f(3a ). 4 9a + 2 6a – 14 21B Determine whether the relation is a function. Yes. Every x is paired with one y. 21CDetermine whether the relation is a function. No. A vertical line crosses the graph more than once. 22A Find the measure of angle BAC. 55˚ 22B Find the measure of angle DBC. 130˚ 22C Find the measure of angle 3. 42˚ 23A If angle one measures 40˚and angle two measures 60˚find the measure of angle four. 100˚ 23B Find x. 75 23C 58 Find x. 24A Find the value of r so that the line through (r,6) and (10,-3) has a slope of -3/2. r=4 24B Find the slope of the line that passes through the points (-1, 2) and (3, 4). 1/2 24C Find the rate of change for 1990-2000. $13.7 billion 25A Which postulate can be used to prove ∆ABD is congruent to ∆ACD. SAS 25B Complete the congruence statement and the postulate or theorem that applies. ∆MIN by SAS which postulate can be 25C Determine used to prove that the triangles are congruent. SAS or SSS 26A Complete the congruence statement and the postulate or theorem that applies. ∆VNR, AAS or ASA 26B a. b. c. d. e. Given Given Reflexive Property AAS CPCTC 26C Complete the congruence statement and the postulate or theorem that applies. ∆VMN by ASA or AAS 27A Determine which postulate can be used to prove that the triangles are congruent. If it is not possible to prove that they are congruent, write not possible. HL 27B When is SSA a valid test for triangle congruence? When the angle is right. (HL) 27C Determine which postulate can be used to prove that the triangles are congruent. If it is not possible to prove that they are congruent, write not possible. SAS 28A A 28B What is the measure of angle ABF? 28˚ 28C Find x. 18 29A A is the centroid of Find x. x=4 DEF. 29B x = 24 29C C 30A Determine which angle has the greatest measure. angle two 30B Use the Exterior Angle Inequality Theorem to list all angles whose measures are greater than the measure of angle six. angle one and angle seven 30C Determine the relationship between the measures of the angles. mWXY mXYW 31A Write the assumption you would make to start an indirect proof of the statement. A median of an isosceles triangle is also an altitude. A median of an isosceles triangle is not an altitude. 31B Write the assumption you would make to start an indirect proof of the statement. Points P, Q are R are collinear. Points P, Q are R are noncollinear. 31C Write the assumption you would make to start an indirect proof of the statement. The angle bisector of the vertex angle of an isosceles triangle is also an altitude of the triangle. The angle bisector of the vertex angle of an isosceles triangle is not an altitude of the triangle. 32A Find the range for the measure of the third side of a triangle given the measures of two sides are 7 and 12. 5<n<19 32B Solve b 25. 7 Then check your solution. {b l b ≥ 175} 32C Solve 2 p 14. 5 p> - 35 33A Solve the inequality: 5(2h – 6) – 7(h + 7) >4h h < -79 33B Solve: 3d – 2(8d – 9) > 3 – (2d+7) {d l d < 2} 33C Solve: 8(t + 2) – 3(t – 4) < 5(t – 7) + 8 Ø 34A Determine whether the pair of figures is similar. Justify your answer. 34B Triangle ABC is similar to ∆XYZ with a scale factor of 2/3. If the lengths of the sides of ∆ABC are 6, 8, and 10 inches, what are the lengths of the sides of ∆XYZ ? x=9 y=12 z=15 34C Find x. 1.6 35A Find x and AB. x = 1.5, AB = 3 35B How tall is the tower? 420.5 m 35C Find the height of the tree. 10.75 m 36A Graph: (1/2)x – y > 4 36B Graph: 4y + 2x ≥ 16 36C Graph: y > 3 + ½ x 37A Find x. 3 2 37B Find x and y. x = 3 y =3 2 37C Find x and y. x =5 2 y=5 2 38A Find a and c. a =6 3 c=6 38B Find a and b. a= 12 3 b=12 38C Find a and c. a=7 3 c=14 39A Find sine of angle S. 3/5 = 0.6 39B Find x. Round to the nearest tenth. 8.5 39C Find x. Round to the nearest tenth. 44.9 40A Use elimination to solve the system of equations. 3x - 4y = -10 5x + 8y = -2 (x,y) = (-2,1) 40B Use elimination to solve the system of equations. 3x + 4y = 6 5x + 2y = -4 (-2, 3) 40C Use elimination to solve the system of equations. 3x + 4y = -25 2x - 3y = 6 (-3, -4) 41A Find the sum of the measures of the interior angles of a dodecagon. 1800 41B Find the sum of the measures of the interior angles of a 32-gon. 5400 41C Find the number of sides of a regular polygon with an interior angle of 140˚. 9 42A Two consecutive angles of a parallelogram measure (3x + 42)˚ and (9x – 18)˚. Find the measures of the angles. 81˚ and 99˚ 42B What are the coordinates of the intersection of the diagonals of parallelogram ABCD with vertices A (2,5), B(6,6), C (4,0), and D (0, -1)? (3, 2.5) 42C Quadrilateral LMNP is a parallelogram. Find the measure angle PLM, the measure of angle LMN and d. angle PLM= 108˚ angle LMN= 72˚ d = 11 43A Find x so that the quadrilateral is a parallelogram. x = 12 43B Determine whether the quadrilateral is a parallelogram. Justify your answer. Yes. Opposite angles are congruent. 43C Find x and y so that the quadrilateral is a parallelogram. x = 8 y = 1 1/3 44A Arrange the terms of the polynomial so that the powers of x are in descending order. 3 2xy 3 5x + – 2 y 3 +5x 2 3x y + – 2 3x y 3 2xy + 2 y 44B Find the degree of the polynomial. 11r2t4 – 2s4t5 + 24 9 44C Arrange the terms of the polynomial so that the powers of x are in descending order. 2 3xy – 6y + 2 3xy 3 4x 2 +x y + + 6y 2 xy – 3 4x 45A Determine whether parallelogram ABCD is a rhombus, a rectangle, or a square. square 45B Use rhombus QRTS to find 28 45C Use rhombus QRTS to find y = ± 11 46A 8 46B median = 14 measure of angle W=110 measure of angle Z=110 46C What type of quadrilateral is WXYZ? Justify your answer. Trapezoid One pair of opposite sides is parallel. 47A Reflect triangle DFG over the x axis. 47B Reflect triangle DFG over the y axis. 47C Reflect triangle DFG over the line y = x. 48A Rectangle PQRS has vertices P(-3,5), Q(-4,2), R(3, 0), and S (4, 3). Graph PQRS and its image for the translation (x,y) (x+8, y-5) 48B Find the product. (6p - 1)2 2 36p – 12p + 1 48C Find the product. (3n – 2) (3n + 2) 2 9n -4 49A B 49B Copy ∆ACC and rotate the triangle 60˚counter clockwise about point G. 49C A five-disc CD changer rotates as each CD is played. Identify the magnitude of the rotational symmetry as the changer mover form one CD to another. 72˚ 50A Factor the polynomial. x3y2 + x x(x2y2 + 1) 50B Solve. Check your solutions. x(x-24) = 0 {0, 24} 50C Factor the polynomial. 24m2np2 + 36m2n2p 12m2np(2p + 3n) 52A Find the circumference of a circle with a radius of 7cm. C = 2πr 14π ≈ 43.98 cm 52B Find the circumference of a circle with a diameter of 12.5 cm. C = πd 12.5π ≈ 39.27 in. 52C Find the exact circumference of circle P. C = πd 13π cm 51A Find the measure of the dilation image using the scale factor r= -2. 51B 51C Determine the scale factor for the dilation with center C. Then determine whether the dilation is an enlargement, reduction, or congruence transformation. enlargement 53A Find 140˚ . 53B Find . 230˚ 53C 10π≈31.42 units 54A Determine the measure of each arc of the circle circumscribed about the traffic sign. 45˚ 54B Find . 80˚ 54C Find 40˚ .. 55A Find the measure of angle 1 and angle 2. 30˚ 55B Find the measure of angle 3 and angle 5. 50˚ 55C Quadrilateral ABCD is inscribed in circle P. If angle B measures 80˚ and angle C measures 40˚, find the measure of angle A and angle D. Measure of angle A = 140˚ Measure of angle D = 100˚ 56A Find x. Assume that NP is tangent to circle O. 8 56B 56C x=4 57A 155˚ 57B 129˚ 57CFind x. 35˚ 58A Find x. x=2 58B Find RS is PQ = 12, QR = 2, and TS = 3. x=4 58C Find x. Assume that segments that appear to be tangent are tangent. hint b b 4ac x 2a 2 ≈ 2.37 59A Write the equation of a circle with center at (-2, 4) and diameter 4. 59B Write the equation of the circle with center at (-3, 5), radius 10. 2 (x+3) + 2 (y-5) = 100 59C Write the equation of the circle with center at the origin, radius 7 2 x + 2 y = 7 60A Find the area and perimeter of the parallelogram. Units are in millimeters. Area = 415.7 mm2 Perimeter = 88mm 60B Find the perimeter and area of the parallelogram. Round to the nearest tenth if necessary. perimeter: 80 in. area: 259.8 in2 60C Find the perimeter and area of the parallelogram. Round to the nearest tenth if necessary. perimeter: 46 yd Area: 91.9 yd2 61A Find the area of the trapezoid. Units are in yards. 180 2 yd 61B Find the area of the triangle. 12.41 cm2 61C Find the area of the rhombus. 1200 ft2 62A Find the area of a regular pentagon with a perimeter of 40 cm. A = ½ Pa 110 2 units 62B Find the area of the shaded region. Round to the nearest tenth. 114.2 2 units 62C A square is inscribed in a circle of area 18π square units. Find the length of a side of the square. 6 units 63A Find the area of the figure. Round to the nearest tenth. 366.7 2 units 63B Find the area of the figure. 4185 2 units 63C Find the area of the figure. Round to the nearest tenth. 154.1 2 units 64A What is the chance that a dart thrown at the board will land on a white stripe? 5/12 64B Find the area of the blue sector. 4.6 π 64C Find the probability that a point chosen at random lies in the blue region if the area of the blue region is 4.6 π. .13 or 13% 65A Which net could be folded into a pyramid if folds are made only along the dotted lines. 65B Which shape cannot be folded to make a pyramid? 65C Which shape could be folded into a rectangular prism if folds are made along the dotted lines? 66A Find the lateral area of the regular pentagonal prism. 560 2 cm 66B Find the surface area. 318 2 units 66C Find the surface area. 336 2 units 67A Find the surface area of the cylinder. ≈777.0 2 ft 67B Find the surface area of the cylinder. Round to the nearest tenth. 251.3 2 ft 67C Find the surface area of the cylinder. Round to the nearest tenth. 291.1 2 yd 68A Are the triangles similar? Yes 68B Find the surface area of the square pyramid. 68C Find the surface area of the prism. Round to the nearest tenth. 423.9 2 cm 69A Find the lateral area of the cone. Use 3.14 for π. Round to the nearest tenth. Units are in feet. 109.9 2 ft 69B Find the surface area of the cone to the nearest tenth. 270.2 2 cm 70A Find the surface area of the sphere given the area of the great circle. 804.4 in. 2 69C Find the surface area of the cone. Round to the nearest tenth. 301.6 2 ft 70B Find the surface area of the sphere. Round to the nearest tenth. 7854.0 in 2 70C Find the surface area of a baseball with a circumference of 9 inches to determine how much leather is needed to cover the ball. 25.8 2 in 71A Find the volume of the triangular prism. V=Bh AT= ½ bh 780 3 cm 71B Find the volume of the cylinder. V=Bh AC=πr2 3 ≈824.3m 71C Find the volume of the oblique cylinder. V=Bh AC=πr2 ≈452.4 3 yd 72A Find the volume of the pyramid. V= 1/3 Bh AR = lw 640 3 in 72B Find the volume of the cone. V=1/3Bh AC=πr2 ≈536.2 3 in 72C Find the volume of the oblique cone. V=1/3Bh AC=πr2 ≈ 929.4 3 in 73A Are the two triangles similar? Yes 73A Find the volume of the sphere. 4 3 V r 3 57,905.8 3 in 73B Find the volume of the hemisphere. 14 3 V r 23 16.8 3 ft 73C Compare the volume of the sphere ant eh cylinder. Determine which quantity is greater. The volume of the cylinder is greater.