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Quarterly 2 Test Review For #1-5, choose the method used to prove the triangles congruent. HL SAS AAS SSS ASA 1. οA and οD are right οβs; π΄π΅ β π΅π· HL Thm 2. π΄π΅ β π΅π·; π΄πΆ β πΆπ· SSS Post. 3. οA and οD are right angles; π΄π΅ β π·πΈ AAS Thm 4. C is the midpoint of π΅π· and π΄πΈ SAS Post. 5. πΆπ΅ bisects οACD; πΆπ΅ β₯ π΄π· ASA Post. 6. Complete the following proof by filling in the missing reasons. Given: β B β β C; M is the midpoint of π΅πΆ Prove: π΄π΅ β π·πΆ STATEMENTS REASONS 2. M is the midpoint of π΅πΆ Given Given 2.______________________ 3. π΅π β πΆπ Def. of midpoint 3.______________________ 4. β AMB β β CMD Vertical β βs are β . 4.______________________ 5. βAMB β βDMC ASA Postulate 5.______________________ 6. π΄π΅ β π·πΆ CPCTC 6.______________________ 1. β B β β C 1. ______________________ 7. In an isosceles ABC, π΅πΆ is the base and mβ B = 42°. Find mβ A and mβ C. A B 42° 42° mβ C = 42° mβ A = 96° C 8. If two parallel lines are cut by a transversal, then β corresponding angles are ____________. 9. If two parallel lines are cut by a transversal, then β alternate interior angles are _________. 10. If two parallel lines are cut by a transversal, supplementary then same-side interior angles are _____________. 11. A median of a triangle is a segment from the midpoint vertex to the ________________ of the opposite side. altitude 12. A(n) ___________ of a triangle is a segment from a vertex perpendicular to the opposite side. 13. A perpendicular bisector of a segment is a perpendicular line (or ray or segment) that is ______________ midpoint to the segment as its ______________. For #14-18, answer with always, sometimes, or never. never 65°. 14. If ΞABC is equiangular, then mβ B is __________ always 15. In any triangle, there is ______________ at least two acute angles. 16. If two parallel lines are cut by a transversal, then always congruent. corresponding angles are __________ sometimes right. 17. If a triangle is isosceles, then it is ____________ always 18. The acute angles of a right triangle are __________ complementary. For #19 and 20, answer with true or false. 19. A triangle may have the sides measuring 12, 28, 40. FALSE; 12 + 28 = 40 20. In right triangle ABC, If mβ A = 90°, then π΄πΆ is the longest side. B FALSE A C 21. Find x. 3x + 85 = 8x 85 = 5x x = 17 22. What is the interior angle sum of a decagon? (n β 2)180 (10 β 2)180 1440° 23. What is the exterior angle sum of a decagon? 360° 24. What is the measure of each interior angle of a regular decagon? π β2 180 144° int β = π 25. What is the measure of each exterior angle of a 360 regular decagon? ext. β = π 36° 26. What polygon has an interior angle measuring 135°? π β2 180 octagon int β = π 27. List the angles from greatest to smallest. β D, β F, β E 28. List the sides from greatest to smallest. ππ, ππ, ππ 29. If point O lies in the interior of οABC, then OBC mοABC = mοABO + mο____________. A (hint: Draw your own picture.) O B C 30. If point O does not lie on straight angle ABC, 180 then mοABO + mοCBO = _____°. (hint: Draw your own picture.) O A B C 31. In the diagram, π΄πΆ β₯ π΅π·, mβ DBE = (x β 8)° and mβ EBC = (3x + 2)°. Find x. 3x + 2 x β 8 + 3x + 2 = 90 4x β 6 = 90 4x = 96 x = 24 For # 32 β 35, name the property is used. 32. If a = b and b = c, then a = c. Transitive Property 33. If a = b, then b = a. Symmetric Property 34. a = a Reflexive Property 35. If a = b and a + c = d, then b + c = d. Substitution Property 36. If two lines intersect, then their intersection point is a ______________. 37. If two planes intersect, then their line intersection is a ______________. 38. If mβ ROS = (6x + 3)° and mβ TOP = (8x - 7)°, 5 then x = ____. 8x β 7 = 6x + 3 x=5 39. X is the midpoint of ππ. If WX = (3x), XZ = (x + 6), then find x. x+6 3x 3x = x + 6 2x = 6 x=3 For #40 - 46, a || b and mβ 1 = 75°. corresponding angles. 40. β 1 and β 5 are _______________ s-s interior 41. β 2 and β 6 are _______________ angles. alt. interior 42. β 5 and β 6 are _______________ angles. 105° 43. mβ 2 = ________ 105° 44. mβ 3 = ________ 75° 45. mβ 5 = ________ 75° 46. mβ 5 = (6x + 2)° and mβ 6 = (8x β 10)°. Find x. 6x + 2 = 8x β 10 12 = 2x x=6 47. What is the image of P(3, β5) using the translation (x, y) β (x + 4, y β 6)? Pβ(3 + 4, β5 β 6) Pβ(7, β11) For #48-51, use the coordinate plane to the right. 48. What is the image of P(1, 4) if (x, y) is reflected in the yβaxis? Pβ(β1, 4) 49. What is the image of P(1, 4) if (x, y) is reflected in the x-axis? Pβ(1, β4) 50. What is the image of P(1, 4) if (x, y) is reflected in the line y = x? Pβ(4, 1) 51. What is the image of P(1, 4) if (x, y) is reflected in the line y = βx? Pβ(β4, β1) For #52 β 54, describe the transformation shown. 52. translation (x, y) β (x + 2, y β 8) 53. reflection over x-axis 54. rotation about the origin 180° clockwise or counterclockwise STUDY