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Version A Geometry Midterm Name: _________________________________________ Class: _________________________________________ Date: _________________________________________ 1. Determine if the two shapes are congruent and explain why? A. No, becuase no angles are congruent. B. Yes, it was reflected across the x-axis and rotated 180 degrees. C. No, because not all sides are congruent. D. Yes, it was rotated 180 degrees about the origin. 2. is rotated about point C in a clockwise direction. What is the relationship between and its image ? A. They are congruent. B. Each side of A'B'C' is 45 times as large as the sides of ABC. C. Each angle of A'B'C' is 45 degrees larger than each angle of ABC. D. The two triangles have no relationship to each other. Version A 3. These two triangles are congruent. If side AD = 3 and side BC = 4, then what is the length of side AB? A. 3 cm B. 4 cm C. 5 cm D. 7 cm 4. The following statements are true: "a" is congruent to "d" "b" is congruent to "e" What reason makes the two triangles congruent? A. SSS postulate B. SAS postulate C. ASA postulate D. AAS postulate Version A 5. Are the following triangles congruent? Which postulate supports your statement? A. No, the triangles are not congruent. B. Yes, because of ASA. C. Yes, because of SSA. D. Yes, because of SAS 6. In this diagram, congruent to is perpendicular bisector of . Which theorem would justify Step 6? A. AAS B. ASA C. SAS D. SSS . The two-column proof shows that is Version A 7. In this diagram, STU is an isosceles triangle where shows that is congruent to . is congruent to . The paragraph proof Which step is missing in the proof? A. CPCTC B. Reflexive Property of Congruence C. Definition of right angles D. Angle Congruence Postulate 8. Using only the information presented in the diagram, determine if the following triangles are congruent, and state which congruence postulate was used. A. The triangles are congruent by ASA. B. The triangles are congruent by SAS. C. The triangles are congruent by SSA. D. The triangles are not congruent. Version A 9. Parallelogram FGHJ was translated 3 units down to form parallelogram F'G'H'J'. Parallelogram F'G'H'J' was then rotated counterclockwise about point G' to obtain parallelogram F"G"H"J". Which statement is true about parallelogram FGHJ and parallelogram F"G"H"J"? A. The figures are both similar and congruent. B. The figures are neither similar nor congruent. C. The figures are similar but not congruent. D. The figures are congruent but not similar. Version A 10. Kaz went camping with his friend Dillion. They put together the tent first, starting with the frame. The canvas they put over the frame formed a angle with the ground. The center pole was 4 feet off the ground and it stood perpendicular to the ground. Using only the information presented, which postulate could be used to prove that the sides of the tent are equal in length? A. AAS B. SAS C. ASA D. They are not equal. Version A 11. In hexagon DRAGON the diagonals writing a proof to show the and bisect each other. Jared's geometry class is . The teacher asks Jared to justify step three. What should he answer? A. Adjacent angles are congruent. B. Vertical angles are congruent. C. Alternate Interior angles are congruent. D. Definition of angle bisector. Version A 12. Given Prove: and . are supplementary. In the proof, what is the reason for statement 6? A. If two lines are cut by a transversal, and the alternate interior angles are congruent, then the lines are parallel. B. If two lines are cut by a transversal, and the same-side interior angles are congruent, then the lines are parallel. C. If two lines are cut by a transversal, and the alternate exterior angles are congruent, then the lines are parallel. D. If two lines are cut by a transversal, and the corresponding angles are congruent, then the lines are parallel. 13. Jared is writing an arguement to prove that the base angles of an isosceles triangle are congruent. He begins by drawing the angle bisector of the vertex angle. Which of the following will NOT BE NECESSARY for Jared to use in writing his proof? A. Angle sum theorem for triangles. B. SAS Postulate C. Reflexive Property D. CPCTC Version A 14. What reason would replace the question mark to correctly complete the proof? A. Reflexive Property. B. Symmetric Property. C. Substition. D. Transitive. Version A 15. What is the scale factor in the given image? A. 2 B. 1 C. 0.5 D. 0.25 16. What is the relationship of the corresponding sides of the dilated figure? A. The corresponding sides of dilated figures are parallel. B. The corresponding sides are dilated by a scale factor of 3. C. The corresponding sides are congruent. D. The corresponding sides of a dilated figure are congruent. Version A 17. A triangle is enlarged with a scale factor of two. In the enlargement you would expect to find that ... A. the area was twice as much as the original. B. the sides were twice as long as the original. C. the angles were twice the size of the original. D. the sides were half as long as the original. 18. The dashed triangle is a dilation image of the solid triangle. What is the scale factor? A. B. C. D. 2 19. The sides of a triangle are 5, 6, and 10. Find the lenght of the longest side of a similar triangle whose shortest side is 15. A. 10 B. 15 C. 18 D. 30 Version A 20. A carpenter is building a custom wall unit, as shown in the scale drawing. Because are right angles the two angles are congruent. By the Reflexive Property, So and are similar by which reason below? A. AA B. AAS C. ASA D. SSS 21. Which explains why the triangles below are similar? A. AA B. ASA C. SSS D. AAS and Version A 22. Sarah wants to prove the Pythagorean Theorem using similar triangles. She asks for your help in identifying the similar triangles. Choose the correct similarity statement, based on the given picture. A. B. C. D. 23. Which of these statements, if true, would be sufficent to prove that triangles SRT and PQR are similar? A. B. C. D. Version A 24. is the mid-segment of . Which of the following is a false statement? A. DE=2BC B. AD=EC C. 2DE=BC D. 25. is the mid-segment of and . If AD=3 cm and AE=4 cm, then: A. BC = 14 cm B. BC = 10 cm C. BC = 8 cm D. BC = 6cm 26. At the same time of the day, a man who is 76 inches tall casts a 57 inch shadow and his son casts a 24 inch shadow. What is the height of the man's son? A. 32 B. 33 C. 81 D. 108 27. Determine the length of A. B. C. D. if is (3z+2) units. Version A 28. Which triangle congruence criteria will determine congruence for the given diagram? A. SSS B. SAS C. ASA D. AAS E. HL 29. To be able to prove that by SAS, using the two given congruent corresponding sides, one piece of information is missing. Which of the following would be that piece of information? A. Base angles of an isosceles are congruent B. bisects C. D. 30. is a right angle Three of the four items listed can be used to establish congruence by SAS. Determine which one is NOT needed to prove by SAS? A. B. C. D. Version A 31. Given & and , , then . A. True B. False 32. In right triangle ABC, angle A and angle B are complementary angles. The values of cos A is . What is value of sin B? A. B. C. D. 33. In right triangle HJK, be true? A. B. C. D. is a right angle and . Which statement about triangle HJK must Version A 34. A 12-foot ladder is leaning against a building at a angle with the ground. Which can be used to find how high the ladder reaches up the side of the building? A. B. C. D. 35. Find the missing angle. A. B. C. D. 36. Find the missing angle. A. B. C. D. Version A 37. Find the missing side. A. 23.3 B. 9.2 C. 7.5 D. 27.9 38. Find the missing side. A. 4.0 B. 6.3 C. 38.4 D. 5.9 39. A hot air balloon is 1200 feet above the ground. The angle of depression from the basket of the hot-air balloon to the base of a monument is . Which equation can be used to find the distance, d, in feet, from the basket of the hot-air balloon to the base of the monument? A. B. C. D. Version A 40. How are the circles related? A. They are congruent. B. They are similar. C. The radius are congruent. D. The circles are not similar.