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Name ________________________Period ___ Score_____=______ Notes _____________ 10 70 C/B ________________________________ 7th Grade Accelerated Chapter 9 & 10 Review 1. Points E, F, G, and H are all in plane S. Can and be skew?__________Explain your reasoning. ______________________________________________________________________________ 2. The measure of is 88 Ray BD bisects . What are the measures of and ? ______ Are these two angles congruent? ____________Explain._________________________________________ _________________________________________________________________________________ 3. 3. Line segment XY has a length of 16 units. Point Z is the midpoint of . Point V is the midpoint of the length of ? _____________What line segment is congruent to ?________________ . What is 4. Write the order of the side lengths from largest to smallest. _____, ______, ______ 5. Triangle HIJ is congruent to . The measure of is 32, the measure of is 62, and the measure of is 86. What are , , and ? ___________Explain your reasoning._______ ________________________________________________________________________________________ __ 6. A circle with center E and line segments have been drawn. The lengths of , , and are all different from each other. Is it possible for points F, G, and H to be on the same arc of the circle with center E? _________Explain.________________________________________________________________________ 7. Kevin constructed a triangle that is congruent to . To make sure the new triangle is congruent to he used , , and the included side. Name the side that Kevin used to construct the new triangle. , ________________ 8. The measure of is 64. Ray RT bisects . What are the measures of and ?_______ Are these two angles congruent?___________ Explain.__________________________________________ __________________________________________________________________________________________ 9. The measure of is 23. What is the measure of an angle supplementary to the measure of an angle complementary to ?___________________________ 10. The figure shown includes pairs of supplementary angles and pairs of vertical angles. ? __________What is a. The measure of is 85. What are , __________ ,___________ and ?____________ Explain your reasoning.____________________________________________________________________ b. The measure of linear pair. is 80. Name a linear pair that includes . Write the measure of each angle in the 11. 88 mm, 97 mm, 92 mm. Determine whether it is possible to form a triangle using the set of segments with the given measurements. Explain your reasoning. __________________________________ ______________________________________________________________________________________ Multiple Choice ____ 12. The measure of a. b. c. d. is 68. What is the measure of its supplementary angle? 22 90 112 180 ____ 13. Terry measured an angle with a protractor. She aligned one side with the bottom of the protractor. The other side passes through the mark that reads 110 and 70. The angle is acute. What is the measure of the angle? a. b. c. d. 40 70 110 180 ____ 14. Which of the following has zero width and an infinite length? a. b. c. d. a point a line segment a line a plane ____ 15. A ray bisects an obtuse angle into two congruent angles. What type of angles are these two congruent angles? a. b. c. d. acute right obtuse straight ____ 16. Ray EF contains points G and H. What is the endpoint of a. b. c. d. E F G H ? ____ 17. The midpoint of a. b. c. d. is Y. The length of is 4 centimeters. What is the length of ? 4 cm 6 cm 8 cm 10 cm ____ 18. John measures an angle with a protractor. He aligned one side with the bottom of the protractor. The other side passes through the mark that reads 135 and 45. The angle is obtuse. What is the measure of the angle? a. b. c. d. 45 90 135 180 ____ 19. Line segment AB has a length of 24 units. Point C is the midpoint of the length of ? a. b. c. d. is 57. What is the measure of its complementary angle? 33 90 123 180 ____ 21. Angle A is congruent to a. b. c. d. . What is 6 units 12 units 24 units 48 units ____ 20. The measure of a. b. c. d. Point D is the midpoint of . Angle A measures 60. What is the measure of ? 30 60 120 180 ____ 22. What is the first step to duplicate a given line segment AB? a. b. c. d. Label point C on Draw a starter line. Set your compass at length Place the compass at C. . ____ 23. The lengths of two sides of a triangle are 3 cm and 7 cm. What can you conclude about the maximum length of the third side of the triangle? a. b. c. d. The maximum length of the third side must equal 10 cm. The maximum length of the third side must be greater than 10 cm. The maximum length of the third side must be less than 10 cm. The maximum length of the third side must equal 4 cm. ____ 24. A triangle has angle measures 23 and 35. What is the measure of the third angle? a. 32 b. 90 c. 122 d. 180 ____ 25. Figure GHIJ is congruent to figure NOPQ. What pair of angles must be congruent? a. b. c. d. and and and and ____ 26. What is the measure of a. b. c. d. ? 30 63 147 150 ____ 27. The lengths of two sides of a triangle measure 8 feet and 14 feet. What is the largest whole number value that the third side could measure? a. b. c. d. 21 feet 22 feet 23 feet 24 feet ____ 28. You can construct congruent triangles if you know which of the following? a. b. c. d. the measures of three sides the measures of two angles and one given side the measures of two sides and the included angle all of the above ____ 29. A triangular bike path is exactly 9 miles long. If each of the three connecting paths is a whole-number of miles long, which could be the lengths of the paths? a. b. c. d. 1 mile, 1 mile, 7 miles 1 mile, 2 miles, 6 miles 2 miles, 2 miles, 5 miles 2 miles, 3 miles, 4 miles ____ 30. In the two triangles shown, . Which congruency statement describes the relationship between the two triangles? a. b. c. d. ____ 31. What can you conclude about ACD using the Exterior Angle Inequality Theorem? a. b. c. d. the measure of the measure of the measure of the measure of ACD is less than 121 ACD is greater than 121 ACD is less than the sum of 121 and 17 ACD is greater than the sum of 121 and 17 End of Chapter Test Solve for x. 32. ___________________ 33. Philippe cuts the following three figures out of wood. a. Which two figures appear to be congruent?__________________ b. List the pairs of congruent line segments from the figures you named in part (a).________________ ____________________________________________________ c. List the pairs of congruent angles from the figures you named in part (a)._____________________ __________________________________________________________________________________ 34. Ian, Isabella, Lloyd, and Jason made claims about triangles. Evaluate each of their claims. If one of the claims is false, give an example that disproves the claim. a. Ian says that if the three sides of one triangle have the same length as the three sides of a second triangle, then the two triangles are congruent._______________________________________________________ b. Isabella says if two sides and their included angle on one triangle have the same measures as two sides and their included angle on another triangle, then the two triangles are congruent._________________ ___________________________________________________________________________________ c. Lloyd says that if two angles and their included side on one triangle have the same measures as two angles and their included side on another triangle, then the two triangles are congruent._____________ ____________________________________________________________________________________ d. Jason says that if the three angles on one triangle have the same measure as the three angles on another triangle, then the triangles are congruent.__________________________________________________ ____________________________________________________________________________ Determine whether it is possible to form a triangle using the set of segments with the given measurements. Explain your reasoning. 35. 15 m, 4 m, 10.9 m ___________ ______________________________________________________________ __________________________________________________________________________________________ Determine whether it is possible to form a triangle using the set of segments with the given measurements. Explain your reasoning 36. 7 in., 8.7 in., 15.4 in. ________ ____________________________________________________________ _______________________________________________________________________________________ 7th chapter 9 & 10 Answer Section 1. ANS: No. Line EF and cannot be skew. Line EF must be in plane S because E and F are in plane S. Similarly, must be in plane S because G and H are in plane S. Therefore, the two lines are coplanar, not skew. PTS: 1 REF: 9.1 NAT: 7.G.2 TOP: Pre Test KEY: geometry | protractor | compass | straightedge | sketch | draw | construct | geometric construction | point | line | plane | coplanar lines | skew lines | line segment | endpoints | arc | congruent line segments | congruent | intersection 2. ANS: The measure of is 44 and the measure of is 44. Yes. These two angles are congruent because they have the same measure. PTS: 1 REF: 9.2 NAT: 7.G.2 TOP: Pre Test KEY: ray | angle | sides of an angle | vertex | degrees | acute angle | right angle | obtuse angle | straight angle | congruent angles | bisect | angle bisector 3. ANS: The length of is 4 units. Line segment VZ is congruent to . PTS: 1 REF: 9.3 NAT: 7.G.2 | 7.G.5 TOP: Pre Test KEY: supplementary angles | complementary angles | perpendicular | midpoint of a segment | segment bisector | perpendicular bisector | adjacent angles | linear pair | vertical angles 4. ANS: b, a, c PTS: 1 REF: 10.1 NAT: 7.G.2 TOP: Pre Test KEY: Triangle Sun Theorem | remote interior angles of a triangle | Exterior Angle Theorem | Exterior Angle Inequality Theorem 5. ANS: The measure of is 32, the measure of is 62, and the measure of is 86. Corresponding angles on congruent figures have the same measure. PTS: 1 REF: 10.3 NAT: 7.G.2 TOP: Pre Test KEY: geometric figures | congruent geometric figures | corresponding sides | corresponding angles | included angle | included side 6. ANS: No. Points F, G, and H cannot be on the same arc of the circle with center E because the distance from a circle’s center to any point on the same arc of the circle is the same. PTS: 1 REF: 9.1 NAT: 7.G.2 TOP: Post Test KEY: geometry | protractor | compass | straightedge | sketch | draw | construct | geometric construction | point | line | plane | coplanar lines | skew lines | line segment | endpoints | arc | congruent line segments | congruent | intersection 7. ANS: Kevin used to construct the new triangle. PTS: 1 REF: 10.3 NAT: 7.G.2 TOP: Post Test KEY: geometric figures | congruent geometric figures | corresponding sides | corresponding angles | included angle | included side 8. ANS: The measure of is 32 and the measure of is 32. Yes. These two angles are congruent because they have the same measure. PTS: 1 REF: 9.2 NAT: 7.G.2 TOP: Post Test KEY: ray | angle | sides of an angle | vertex | degrees | acute angle | right angle | obtuse angle | straight angle | congruent angles | bisect | angle bisector 9. ANS: The measure of an angle supplementary to is 157. The measure of an angle complementary to is 67. PTS: 1 REF: 9.3 NAT: 7.G.2 | 7.G.5 TOP: Post Test KEY: supplementary angles | complementary angles | perpendicular | midpoint of a segment | segment bisector | perpendicular bisector | adjacent angles | linear pair | vertical angles 10. ANS: a. Angle 3 is congruent to because they are vertical angles. Therefore, . Both and are supplementary to 1. Both of their measures are equal to , or . So, . b. The linear pair is is 100. and , or and . The measure of is 80, so the measure of both and PTS: 1 REF: 9.3 NAT: 7.G.2 | 7.G.5 TOP: End Ch Test KEY: supplementary angles | complementary angles | perpendicular | midpoint of a segment | segment bisector | perpendicular bisector | adjacent angles | linear pair | vertical angles 11. ANS: Yes. It is possible to form a triangle because , and 180 is greater than 97. 12. 13. 14. 15. 16. 17. PTS: 1 REF: 10.4 NAT: 7.G.2 TOP: End Ch Test KEY: Triangle Inequality Theorem ANS: C PTS: 1 REF: 9.3 NAT: 7.G.2 | 7.G.5 TOP: Standardized Test KEY: supplementary angles | complementary angles | perpendicular | midpoint of a segment | segment bisector | perpendicular bisector | adjacent angles | linear pair | vertical angles ANS: B PTS: 1 REF: 9.2 NAT: 7.G.2 TOP: Standardized Test KEY: ray | angle | sides of an angle | vertex | degrees | acute angle | right angle | obtuse angle | straight angle | congruent angles | bisect | angle bisector ANS: C PTS: 1 REF: 9.1 NAT: 7.G.2 TOP: Standardized Test KEY: geometry | protractor | compass | straightedge | sketch | draw | construct | geometric construction | point | line | plane | coplanar lines | skew lines | line segment | endpoints | arc | congruent line segments | congruent | intersection ANS: A PTS: 1 REF: 9.2 NAT: 7.G.2 TOP: Standardized Test KEY: ray | angle | sides of an angle | vertex | degrees | acute angle | right angle | obtuse angle | straight angle | congruent angles | bisect | angle bisector ANS: A PTS: 1 REF: 9.1 NAT: 7.G.2 TOP: Standardized Test KEY: geometry | protractor | compass | straightedge | sketch | draw | construct | geometric construction | point | line | plane | coplanar lines | skew lines | line segment | endpoints | arc | congruent line segments | congruent | intersection ANS: A PTS: 1 REF: 9.3 NAT: 7.G.2 | 7.G.5 TOP: Standardized Test KEY: supplementary angles | complementary angles | perpendicular | midpoint of a segment | segment bisector | perpendicular bisector | adjacent angles | linear pair | vertical angles 18. ANS: C PTS: 1 REF: 9.2 NAT: 7.G.2 TOP: Standardized Test KEY: ray | angle | sides of an angle | vertex | degrees | acute angle | right angle | obtuse angle | straight angle | congruent angles | bisect | angle bisector 19. ANS: A PTS: 1 REF: 9.3 NAT: 7.G.2 | 7.G.5 TOP: Standardized Test KEY: supplementary angles | complementary angles | perpendicular | midpoint of a segment | segment bisector | perpendicular bisector | adjacent angles | linear pair | vertical angles 20. ANS: A PTS: 1 REF: 9.3 NAT: 7.G.2 | 7.G.5 TOP: Standardized Test KEY: supplementary angles | complementary angles | perpendicular | midpoint of a segment | segment bisector | perpendicular bisector | adjacent angles | linear pair | vertical angles 21. ANS: B PTS: 1 REF: 9.2 NAT: 7.G.2 TOP: Standardized Test KEY: ray | angle | sides of an angle | vertex | degrees | acute angle | right angle | obtuse angle | straight angle | congruent angles | bisect | angle bisector 22. ANS: B PTS: 1 REF: 9.1 NAT: 7.G.2 TOP: Standardized Test KEY: geometry | protractor | compass | straightedge | sketch | draw | construct | geometric construction | point | line | plane | coplanar lines | skew lines | line segment | endpoints | arc | congruent line segments | congruent | intersection 23. ANS: C PTS: 1 REF: 10.4 NAT: 7.G.2 TOP: Standardized Test KEY: Triangle Inequality Theorem 24. ANS: C PTS: 1 REF: 10.1 NAT: 7.G.2 TOP: Standardized Test KEY: Triangle Sun Theorem | remote interior angles of a triangle | Exterior Angle Theorem | Exterior Angle Inequality Theorem 25. ANS: B PTS: 1 REF: 10.3 NAT: 7.G.2 TOP: Standardized Test KEY: geometric figures | congruent geometric figures | corresponding sides | corresponding angles | included angle | included side 26. ANS: D PTS: 1 REF: 10.1 NAT: 7.G.2 TOP: Standardized Test KEY: Triangle Sun Theorem | remote interior angles of a triangle | Exterior Angle Theorem | Exterior Angle Inequality Theorem 27. ANS: A PTS: 1 REF: 10.4 NAT: 7.G.2 TOP: Standardized Test KEY: Triangle Inequality Theorem 28. ANS: D PTS: 1 REF: 10.3 NAT: 7.G.2 TOP: Standardized Test KEY: geometric figures | congruent geometric figures | corresponding sides | corresponding angles | included angle | included side 29. ANS: D PTS: 1 REF: 10.4 NAT: 7.G.2 TOP: Standardized Test KEY: Triangle Inequality Theorem 30. ANS: B PTS: 1 REF: 10.3 NAT: 7.G.2 TOP: Standardized Test KEY: geometric figures | congruent geometric figures | corresponding sides | corresponding angles | included angle | included side 31. ANS: B PTS: 1 REF: 10.1 NAT: 7.G.2 TOP: Standardized Test KEY: Triangle Sun Theorem | remote interior angles of a triangle | Exterior Angle Theorem | Exterior Angle Inequality Theorem 32. ANS: x 64 PTS: 1 REF: 10.1 NAT: 7.G.2 TOP: End Ch Test KEY: Triangle Sun Theorem | remote interior angles of a triangle | Exterior Angle Theorem | Exterior Angle Inequality Theorem 33. ANS: a. Figure ABCDE and figure JKLMN appear to be congruent. b. c. PTS: 1 REF: 10.3 NAT: 7.G.2 TOP: End Ch Test KEY: geometric figures | congruent geometric figures | corresponding sides | corresponding angles | included angle | included side 34. ANS: a. Ian’s claim is true. b. Isabella’s claim is true. c. Lloyd’s claim is true. d. Jason’s claim is false. One triangle could have three angles with the same measures as the three angles of another triangle but have sides that are twice as large as the correspondingsides on the other triangle. PTS: 1 REF: 10.3 NAT: 7.G.2 TOP: End Ch Test KEY: geometric figures | congruent geometric figures | corresponding sides | corresponding angles | included angle | included side 35. ANS: No. It is not possible to form a triangle because , and 14.9 is not greater than 15. PTS: 1 REF: 10.4 NAT: 7.G.2 TOP: Pre Test KEY: Triangle Inequality Theorem 36. ANS: Yes. It is possible to form a triangle because , and 15.7 is greater than 15.4. PTS: 1 REF: 10.4 KEY: Triangle Inequality Theorem NAT: 7.G.2 TOP: Post Test