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3162 Unit 1 Pretest Name___________________________________ MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Solve the problem. 1) Find the measure of the indicated exterior angle. 1) ∠x = (200 - 5n)°, ∠y = (5n + 35)°, ∠z = (n + 11)° A) 110° B) 140° C) 130° 2) What is the measure of the central angle of a regular polygon with 12 sides? A) 30° B) 28° C) 32° D) 165° 2) D) 36° 3) Find the measure of the indicated exterior angle. 3) ∠x = (4n - 20)°, ∠y = (n + 10)°, ∠z = (133 - 6n)° A) 102° B) 145° C) 55° D) 122° 4) If each angle of a regular polygon measures 140°, how many sides does it have? A) 7 sides B) 3 sides C) 9 sides D) 11 sides 4) 5) How many triangles are formed in a regular polygon with 13 sides? A) 13 B) 10 C) 11 5) D) 12 6) Find the measure of the indicated exterior angle. 6) ∠x = (197 - 5n)°, ∠y = (5n + 21)°, ∠z = (n + 11)° A) 174° B) 148° C) 105° D) 122° 7) Find the measure of the indicated exterior angle. 7) ∠x = (4n - 20)°, ∠y = (n + 10)°, ∠z = (130 - 5n)° A) 110° B) 60° C) 126° 1 D) 150° 8) The vehicle shown in the figure is 16 ft long. How long is the trailer? A) 48 ft C) 32 ft B) 8 ft D) Cannot determine 9) What is the angle sum of a regular polygon with 7 sides? A) 900° B) 1350° C) 1260° Determine whether the triple of numbers can be the sides of a right triangle. 10) 7, 10, 17 A) Yes B) No 11) 9, 12, 16 A) Yes 12) 10, 13, A) Yes 8) 9) D) 450° 10) 11) B) No 23 12) B) No 13) 5, 12, 14 A) Yes 13) B) No 2 Use the properties of parallel lines to solve the problem. 14) In the figure, GH DE . Identify any pairs of congruent angles. A) B) C) D) ∠EDF ≅ ∠DFE, ∠GFH ≅ ∠HFG, ∠DEF ≅ ∠FGH, ∠DFG ≅ ∠EFH ∠EDF ≅ ∠HFG, ∠DFE ≅ ∠GHF, ∠DEF ≅ ∠FGH, ∠DFG ≅ ∠EFH ∠EDF ≅ ∠FED, ∠DFE ≅ ∠HFG, ∠FHG ≅ ∠FGH, ∠DFG ≅ ∠EFH ∠EDF ≅ ∠GHF, ∠DFE ≅ ∠HFG, ∠DEF ≅ ∠FGH, ∠DFG ≅ ∠EFH 15) Given BC DE and m∠ABC = 48°, find the measures of as many other angles as possible. A) B) C) D) 14) 15) m∠ADE = m∠ACB = m∠AED = 48°, m∠DBC = m∠ECB = 132° m∠ADE = m∠ACB = m∠AED = 48° m∠ADE = 48°, m∠DBC = 132° m∠ADE = 48°, m∠DBC = m∠ECB = 132° 16) If m n and m∠6 = 117°, what are the measures of the other angles? A) m∠2 = m∠4 = m∠8 = 117°, m∠1 = m∠3 = m∠5 = m∠7 = 63° B) m∠5 = m∠7 = m∠8 = 117°, m∠1 = m∠2 = m∠3 = m∠4 = 63° C) m∠2 = m∠4 = m∠8 = 117°, m∠1 = m∠3 = m∠5 = m∠7 = 27° D) m∠2 = m∠4 = m∠8 = 117°, m∠1 = m∠3 = m∠5 = m∠7 = 73° 3 16) 17) Given AB CD and m∠ABC = 64°, find the measures of angles ∠ABE, ∠FCD, and ∠BCD. A) m∠BCD = 64°, m∠ABE = m∠FCD = 116° C) m∠BCD = 64°, m∠ABE = m∠FCD = 26° 17) B) m∠BCD = m∠ABE = m∠FCD = 26° D) m∠BCD = m∠ABE = 64°, m∠FCD = 116° 18) If p q and m∠8 = 52°, what are the measures of the other angles? 18) A) m∠2 = m∠4 = m∠6 = 52°, m∠1 = m∠3 = m∠5 = m∠7 = 138° B) m∠5 = m∠6 = m∠7 = 52°, m∠1 = m∠2 = m∠3 = m∠4 = 128° C) m∠2 = m∠4 = m∠6 = 52°, m∠1 = m∠3 = m∠5 = m∠7 = 128° D) m∠2 = m∠4 = m∠6 = 52°, m∠1 = m∠3 = m∠5 = m∠7 = 38° 19) In the figure, AB CD. Identify all pairs of congruent angles. A) ∠ABE and ∠FCD C) ∠ABC and ∠FCD, ∠ABE and ∠BCD B) ∠ABE and ∠ABC, ∠FCD and ∠BCD D) ∠ABE and ∠FCD, ∠ABC and ∠BCD 4 19) Provide an appropriate response. 20) Suppose that a given parallelogram is not a rhombus. Which of the following can you conclude about this parallelogram? A) Its sides are not all congruent. B) Its diagonals are perpendicular bisectors of each other. C) It is a square. D) All of the above 20) 21) True or false? In every triangle, the centroid, incenter, and circumcenter are collinear. A) True B) False 21) 22) What is line t called? 22) A) Traversable B) Trisector C) Tangent D) Transversal 23) Is it always true, sometimes true, or never true that the orthocenter is outside its associated triangle? A) Always true B) Sometimes true C) Never true 23) 24) Consider ∠AEF and ∠LEK. What can you conclude about these angles? 24) A) They are obtuse angles. C) They are a pair of vertical angles. B) They are congruent angles. D) All of the above 25) Suppose that a given parallelogram is not a square or a rectangle. Which of the following can you conclude about this parallelogram? A) It is a rhombus. B) It is a kite. C) It is a trapezoid. D) None of the above 25) 26) Which point of concurrency in a triangle is the center of a circle that contains the vertices of the triangle? A) circumcenter B) incenter C) centroid D) orthocenter 26) 5 27) True or false? Any three points are coplanar. A) True 27) B) False 28) If an 8-inch wide rectangle is to approach the golden ratio, what should its length be? A) 16 in. B) 10 in. C) 13 in. D) 12 in. 28) 29) Which basic geometric idea is suggested by a spoke in a bicycle wheel: a ray, a line, a line segment, or an angle? A) Ray B) Line C) Line segment D) Angle 29) 30) Choose the word "rectangle," "square," or "rhombus" to fill in the blank and make the statement true. (If none of the words can be used, then write "none.") 30) A parallelogram is a __________ if and only if it has four congruent sides,its diagonals bisect the angles. A) square B) rhombus C) rectangle D) none 31) Choose the word "rectangle," "square," or "rhombus" to fill in the blank and make the statement true. (If none of the words can be used, then write "none.") A quadrilateral is a _________ if and only if all of its sides are congruent. A) rhombus B) rectangle C) square 31) D) none 32) What type of figure is formed by joining the midpoints of the sides of a general quadilateral? (Be as specific as possible.) A) rectangle B) square C) parallelogram D) rhombus 32) 33) True or false? A triangle can have more than one obtuse interior angle. A) True B) False 33) 34) Classify the triangle as equilateral, isosceles, or scalene and as right, obtuse, or acute. 34) 10 7 6 A) Isosceles; acute C) Scalene; obtuse B) Isosceles; obtuse D) Scalene; acute 35) True or false? A quadrilateral can have more than two obtuse interior angles. A) True B) False 6 35) 36) Choose the word "rectangle," "square," or "rhombus" to fill in the blank and make the statement true. (If none of the words can be used, then write "none.") A quadrilateral is a _________ if and only if all of its sides are congruent and its diagonals are congruent. A) rectangle B) square 37) List the first seven terms of the Fibonacci sequence. A) 1, 1, 3, 4, 7, 11, 18 C) 1, 2, 3, 5, 8, 13, 21 C) rhombus D) none 37) B) 1, 1, 2, 3, 5, 8, 13 D) 1, 2, 4, 6, 10, 16, 26 38) Describe the polygon as convex, concave, or neither of these. A) Convex 36) B) Concave 38) C) Neither 39) Choose the word "rectangle," "square," or "rhombus" to fill in the blank and make the statement true. (If none of the words can be used, then write "none.") A parallelogram is a __________ if and only if its diagonals are perpendicular bisectors of each other. A) square B) rectangle C) rhombus 39) D) none 40) What is the name for the point where the three altitudes of a triangle are concurrent? A) incenter B) orthocenter C) centroid D) circumcenter 40) 41) What type of figure is formed by joining the midpoints of the sides of a rhombus? (Be as specific as possible.) A) parallelogram B) square C) rectangle D) rhombus 41) Solve the problem. Give your answer to the nearest thousandth if necessary. 42) A long-distance runner runs 3 miles south and then 7 miles east. How far is the runner from the starting point? South ↓ 3 mi A) 10 mi East --7 mi--> B) 7.616 mi C) 4.472 mi 7 D) 8.616 mi 42) 43) The length of a garden is 24 meters, and the width is 7 meters. Find the diagonal distance across the garden. 24 meters 43) 7 meters A) 30 meters B) 26 meters C) 25 meters D) 24 meters 44) The diagram depicts a rope connecting the top of a pole to the ground. The rope is 27 yd long and touches the ground 23 yd from the pole. How tall is the pole? 44) 27 yd ? 23 yd A) 25 yd B) 100 yd C) 7.071 yd D) 14.142 yd Find d in simplest radical form. 45) 8 2 45) A) 16 2 B) 32 C) 16 D) 64 2 46) 46) 3 3 A) 3 2 B) 6 C) 18 D) 6 47) 47) 6 8 A) 14 B) 2 5 C) 10 8 D) 14 48) 48) 8 A) 16 B) 4 C) 8 2 D) 8 3 49) 49) 7 2 A) 7 B) 14 3 3 C) 14 D) 7 3 50) Right square pyramid with equilateral triangular faces 8 50) 8 8 A) 4 2 B) 8 2 C) 8 3 D) 4 3 51) 51) 8 A) 16 B) 4 C) 16 2 9 D) 4 3 52) Cube 52) 6 6 6 A) 3 6 B) 6 2 C) 2 3 D) 6 3 53) 53) 10 A) 10 2 B) 30 C) 10 3 D) 20 Refer to this figure to answer the question. Line DH is parallel to line IM. Line BO is perpendicular to line DH. 54) m∠IJN is 51°. What is the measure of ∠JEF? A) 39° C) 129° B) 51° D) Can't determine 54) 55) m∠IJN is 49°. What is the measure of ∠AEF? A) 49° C) 41° B) 131° D) Can't determine 55) 56) m∠IJN is 55°; m∠IJN = m∠PLM. What is the measure of ∠FGC? A) 35° B) 55° C) 125° D) Can't determine 56) 57) m∠IJN is 57°. What is the measure of ∠DEA? A) 57° C) 123° 57) B) 33° D) Can't determine 10 If the triangles are similar, write a similarity statement and give a reason why they are similar. If you cannot confirm that the triangles are similar, indicate "Not necessarily similar." 58) 58) A) △ABC ~ △DEF, Right Triangle Similarity Theorem B) △ABC ~ △DEF, SAS Similarity Theorem C) △ABC ~ △DEF, AA Similarity Postulate D) Not necessarily similar 59) 59) A) △ABC ~ △DEF, SSS Similarity Theorem B) △ABC ~ △DEF, SAS Similarity Theorem C) △ABC ~ △DEF, Right Triangle Similarity Theorem D) Not necessarily similar 60) 60) A) △ABC ~ △DEF, AA Similarity Postulate C) △ABC ~ △DEF, SAS Similarity Theorem B) △ABC ~ △DEF, SSS Similarity Theorem D) Not necessarily similar 61) 61) A) △ABC ~ △DEF, SSS Similarity Theorem B) △ABC ~ △DEF, SAS Similarity Theorem C) △ABC ~ △DEF, Right Triangle Similarity Theorem D) Not necessarily similar 11 Refer to the figure and determine whether the statement is true or false. 62) HD and AB are intersecting lines. A) True B) False 62) 63) KA and KF are parallel lines. A) True B) False 64) Points D, G, and C are collinear. A) True B) False 63) 64) 65) HG and BF are skew lines. A) True 65) B) False 66) Points A, E, B, and C are coplanar. A) True B) False 66) Give an appropriate answer. 67) Find a traversable path that begins at vertex E. 67) A) E → D → A → C → B → A → F → E → B C) E → D → A → B → C → A → F B) E → F → A → B → C → A → D → E D) No such path exists. 12 68) Find a traversable path that begins and ends at vertex A. A) A → B → D → C → E → D → A C) A → D → B → A → C → E → D → C → A 68) B) A → B → D → E → C → A D) No such path exists. Refer to the figure and provide an appropriate name for the indicated angle(s). 69) ∠6 and ∠7 A) Alternate interior angles C) Complementary angles B) Right angle D) Supplementary angles 69) 70) ∠1 and (∠5 + ∠6) A) Alternate exterior angles C) Corresponding angles B) Complementary angles D) Alternate interior angles 71) ∠3 and ∠7 A) Complementary angles C) Supplementary angles B) Alternate interior angles D) Alternate exterior angles 70) 71) 13 Identify the specified angles. 72) All pairs of alternate interior angles 72) A) ∠1 and ∠5, ∠2 and ∠6, ∠4 and ∠8, ∠3 and ∠7 B) ∠4 and ∠5, ∠3 and ∠6 C) ∠1 and ∠7, ∠2 and ∠8 D) ∠4 and ∠6, ∠3 and ∠5 73) All pairs of corresponding angles 73) A) ∠3, ∠4, ∠5, and ∠6 B) ∠1 and ∠5, ∠2 and ∠6, ∠4 and ∠8, ∠3 and ∠7 C) ∠1 and ∠7, ∠2 and ∠8, ∠4 and ∠6, ∠3 and ∠5 D) ∠1 and ∠8, ∠2 and ∠7, ∠4 and ∠5, ∠3 and ∠6 74) All interior angles 74) A) ∠1, ∠6, ∠3, and ∠5 C) ∠1, ∠4 , ∠5, and ∠8 B) ∠1, ∠2 , ∠7, and ∠8 D) ∠2, ∠3, ∠6, and ∠7 14 Which property (if any) should be used to show that the triangles are congruent? 75) A) SAS C) SSS 75) B) ASA D) Not necessarily congruent 76) 76) A) SSS C) SAS B) ASA D) Not necessarily congruent 77) 77) A) AAS C) ASA B) SAS D) Not necessarily congruent 78) 78) 10 5 5 9 10 9 A) SSS C) SAS B) ASA D) Not necessarily congruent 15 Refer to the figure to answer the question. 79) What kind of quadrilateral is DEIH? A) Rhombus B) Kite C) Trapezoid D) Parallelogram 79) 80) What is the vertex of ∠DEI ? A) I B) E C) D D) None 81) Is point J on HI ? A) Yes B) No 82) What are the endpoints of DE ? A) E B) D C) D and E 80) 81) 82) D) None Answer the question. The figure is not drawn to scale. 83) Find the measure of ∠P. 83) 80° 180° A) 260° B) 130° C) 100° D) 50° 84) Find the measure of ∠P. 80° A) 40° 84) B) 160° C) 80° 16 D) 280° 85) Find the measure of ∠P. 110° 85) 70° A) 90° B) 180° C) 20° D) 40° 86) Find the measure of ∠P. 86) 140° A) 140° B) 280° C) 220° D) 70° 87) Find the measure of ∠P. 87) 80° 150° A) 230° B) 35° C) 115° D) 70° 88) Find the measure of ∠P. 88) 60° 140° A) 100° B) 40° C) 80° D) 200° 89) Find the measure of ∠P. 170° A) 50° 89) 70° B) 120° C) 100° 17 D) 240° 90) By how many degrees does m∠P differ from m∠Q? 90) 40° 90° A) 50° B) 20° C) 25° D) 40° 91) Find the measure of ∠P. 200° 91) 50° A) 250° B) 150° C) 125° D) 75° 92) By how many degrees does m∠P differ from m∠Q? 92) 50° 120° A) 70° B) 35° C) 25° D) 50° 93) Find the measure of ∠P. 150° A) 75° 93) B) 300° C) 150° 18 D) 210° Decide whether or not the network is traversable. 94) 94) A) Traversable B) Not traversable 95) 95) A) Traversable B) Not traversable Find the area of the specified figure. 96) △ABC A) 31 square units 96) B) 80 square units C) 40 square units D) 20 square units 97) Parallelogram ABCD A) 15 square units 97) B) 36 square units C) 30 square units D) 18 square units Determine whether the statement is always true, sometimes true, or never true. 98) If the three sides of a triangle are congruent to the corresponding three sides of another triangle, then the triangles are congruent. A) Always true B) Sometimes true C) Never true 19 98) 99) The length of the hypotenuse of a right triangle equals the length of one of the legs of the triangle. A) Always true B) Sometimes true C) Never true 100) If two sides and an angle of a triangle are congruent to the corresponding two sides and angle of another triangle, then the triangles are congruent. A) Always true B) Sometimes true C) Never true 20 99) 100) Answer Key Testname: 3162-UNIT-1-PRETEST 1) C 18) C Objective: (10.3) Find the Measure of an Exterior Angle of Triangle Objective: (10.3) Find Angle Measure Given Parallel Lines II 2) A 19) D Objective: (10.3) Solve Problem Associated with Angles of Polygons Objective: (10.3) Find Angle Measure Given Parallel Lines II 3) C 20) A Objective: (10.3) Find the Measure of an Exterior Angle of Triangle Objective: (10.5) Know Concepts: Quadrilaterals II 21) B 4) C Objective: (10.2) Know Concepts: Points, Segments, and Lines Objective: (10.3) Solve Problem Associated with Angles of Polygons 22) D 5) C Objective: (10.3) Know Concepts: Angles Objective: (10.3) Solve Problem Associated with Angles of Polygons 23) B Objective: (10.2) Know Concepts: Points, Segments, and Lines 6) D Objective: (10.3) Find the Measure of an Exterior Angle of Triangle 24) D Objective: (10.1) Know Concepts: Basic Ideas of Geometry I 7) B Objective: (10.3) Find the Measure of an Exterior Angle of Triangle 25) D Objective: (10.5) Know Concepts: Quadrilaterals II 8) C 26) A Objective: (10.4) Solve Apps: Similar Triangles Objective: (10.2) Know Concepts: Points, Segments, and Lines 9) A Objective: (10.3) Solve Problem Associated with Angles of Polygons 27) A Objective: (10.1) Know Concepts: Basic Ideas of Geometry II 10) A Objective: (10.4) Determine if Sides Form Right Triangle (Y/N) 28) C Objective: (10.1) Use Fibonacci Sequence and Golden Ratio 11) B Objective: (10.4) Determine if Sides Form Right Triangle (Y/N) 29) C Objective: (10.1) Know Concepts: Basic Ideas of Geometry I 12) A Objective: (10.4) Determine if Sides Form Right Triangle (Y/N) 30) B Objective: (10.5) Know Concepts: Quadrilaterals I 13) B 31) A Objective: (10.4) Determine if Sides Form Right Triangle (Y/N) Objective: (10.5) Know Concepts: Quadrilaterals I 32) C 14) D Objective: (10.5) Know Concepts: Quadrilaterals I Objective: (10.3) Find Angle Measure Given Parallel Lines II 33) B Objective: (10.3) Know Concepts: Angles 15) C 34) C Objective: (10.3) Find Angle Measure Given Parallel Lines II Objective: (10.1) Know Concepts: Basic Ideas of Geometry II 16) A 35) A Objective: (10.3) Find Angle Measure Given Parallel Lines II Objective: (10.3) Know Concepts: Angles 36) B 17) A Objective: (10.5) Know Concepts: Quadrilaterals I Objective: (10.3) Find Angle Measure Given Parallel Lines II 1 Answer Key Testname: 3162-UNIT-1-PRETEST 37) B 55) A Objective: (10.1) Use Fibonacci Sequence and Golden Ratio Objective: (10.3) Find Angle Measure Given Parallel Lines I 38) B 56) B Objective: (10.1) Know Concepts: Basic Ideas of Geometry I Objective: (10.3) Find Angle Measure Given Parallel Lines I 39) C 57) C Objective: (10.5) Know Concepts: Quadrilaterals I Objective: (10.3) Find Angle Measure Given Parallel Lines I 40) B 58) C Objective: (10.2) Know Concepts: Points, Segments, and Lines Objective: (10.4) Check for Similarity 41) C 59) C Objective: (10.5) Know Concepts: Quadrilaterals I Objective: (10.4) Check for Similarity 42) B 60) C Objective: (10.4) Solve Apps: Use Pythagorean Theorem Objective: (10.4) Check for Similarity 43) C 61) D Objective: (10.4) Solve Apps: Use Pythagorean Theorem Objective: (10.4) Check for Similarity 44) D 62) B Objective: (10.4) Solve Apps: Use Pythagorean Theorem Objective: (10.1) Identify Geometric Feature in Three-Dimensional Figure (T/F) 45) C 63) B Objective: (10.4) Find Side of 30-60-90 or 45-45-90 Triangle Objective: (10.1) Identify Geometric Feature in Three-Dimensional Figure (T/F) 46) A 64) B Objective: (10.4) Use Pythagorean Theorem to Find Distance in 3D Figure Objective: (10.1) Identify Geometric Feature in Three-Dimensional Figure (T/F) 47) C Objective: (10.4) Use Pythagorean Theorem to Find Distance in 3D Figure 65) A Objective: (10.1) Identify Geometric Feature in Three-Dimensional Figure (T/F) 48) A Objective: (10.4) Find Side of 30-60-90 or 45-45-90 Triangle 66) B Objective: (10.1) Identify Geometric Feature in Three-Dimensional Figure (T/F) 49) B Objective: (10.4) Find Side of 30-60-90 or 45-45-90 Triangle 67) A Objective: (10.2) Find a Traversable Path 50) D 68) D Objective: (10.4) Use Pythagorean Theorem to Find Distance in 3D Figure Objective: (10.2) Find a Traversable Path 69) C 51) B Objective: (10.3) Identify Types of Angles Given Lines I Objective: (10.4) Find Side of 30-60-90 or 45-45-90 Triangle 70) C Objective: (10.3) Identify Types of Angles Given Lines I 52) D 71) B Objective: (10.4) Use Pythagorean Theorem to Find Distance in 3D Figure Objective: (10.3) Identify Types of Angles Given Lines I 72) D 53) C Objective: (10.3) Identify Types of Angles Given Lines II Objective: (10.4) Find Side of 30-60-90 or 45-45-90 Triangle 73) B Objective: (10.3) Identify Types of Angles Given Lines II 54) C 74) D Objective: (10.3) Find Angle Measure Given Parallel Lines I Objective: (10.3) Identify Types of Angles Given Lines II 2 Answer Key Testname: 3162-UNIT-1-PRETEST 75) A 97) B Objective: (10.4) Determine Which Property Shows Congruence Objective: (10.1) Find Area of Polygon 98) A 76) D Objective: (10.4) Know Concepts: Triangles Objective: (10.4) Determine Which Property Shows Congruence 99) C Objective: (10.4) Know Concepts: Triangles 77) C 100) B Objective: (10.4) Determine Which Property Shows Congruence Objective: (10.4) Know Concepts: Triangles 78) A Objective: (10.4) Determine Which Property Shows Congruence 79) C Objective: (10.1) Identify Feature of Figure in a Plane 80) B Objective: (10.1) Identify Feature of Figure in a Plane 81) B Objective: (10.1) Identify Feature of Figure in a Plane 82) D Objective: (10.1) Identify Feature of Figure in a Plane 83) B Objective: (10.3) Find Angle Associated with a Circle 84) A Objective: (10.3) Find Angle Associated with a Circle 85) C Objective: (10.3) Find Angle Associated with a Circle 86) D Objective: (10.3) Find Angle Associated with a Circle 87) C Objective: (10.3) Find Angle Associated with a Circle 88) A Objective: (10.3) Find Angle Associated with a Circle 89) A Objective: (10.3) Find Angle Associated with a Circle 90) D Objective: (10.3) Find Angle Associated with a Circle 91) D Objective: (10.3) Find Angle Associated with a Circle 92) D Objective: (10.3) Find Angle Associated with a Circle 93) A Objective: (10.3) Find Angle Associated with a Circle 94) A Objective: (10.2) Determine If Network Is Traversable 95) B Objective: (10.2) Determine If Network Is Traversable 96) C Objective: (10.1) Find Area of Polygon 3