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Honors Geometry Chapter 4 Review Name: _____________________________________ For numbers 1 – 26, determine whether the statement is true or false. 1. CPCTC means Can Pete cut Tracy’s Chin. F 2. HL has meaning only for right triangles. T 3. An acute triangle is a triangle in which at least two angles are acute. F 4. An obtuse triangle will sometimes have two obtuse angles. T 5. SSS, SAS, ASA are the only ways to prove triangles congruent. F 6. When stating congruent triangles, it doesn’t matter what order you put the letters in. F 7. Two lines that are perpendicular form vertical angles. T 8. If three sides of a triangle are congruent, then it can be called isosceles. T 9. If the base angles of a triangle are congruent, the legs opposite them are congruent. T 10. In a right triangle, the hypotenuse is the side opposite of the right angle. T 11. An equilateral triangle is equiangular triangle. T 12. The side opposite the right angle is called the base. F 13. An acute triangle may have one or more acute angles. F 14. A scalene triangle has no congruent sides. T 15. The base of an isosceles triangle is shorter than a leg of the triangle. F 16. Supplementary angles form a right angle. F 17. If all angles are acute, they form an acute triangle. T 18. Lines drawn in a diagram that are not part of the original diagram are auxiliary lines. T 19. CPCTC stands for Corresponding Parts of Congruent Triangles are Circles. F 20. Every equiangular triangle is isosceles. T 21. If ΔABC ≅ ΔDEF, then AB ≅ EF . F 22. In ΔABC, if ∠B is a right angle, then AC is the hypotenuse of the triangle. T 23. An obtuse triangle has three obtuse angles. F 24. Two triangles are congruent if two sides and an angle of one are congruent to two sides and an angle of the other. F 25. A triangle with two congruent angles is always isosceles. T 26. A right triangle could also be isosceles. T 27. If you were trying to prove ∆ABC ≅ ∆DEF by ASA and were given ∠A ≅ ∠D and ∠C ≅ ∠F, what sides would you need congruent? AC ≅ DF 28. If it is isosceles, then it has at least ___2_____ sides congruent. 29. What triangle congruence postulate is used only for right triangles? HL 30. If FH ≅ FJ , name the base angles. H ∠H ≅ ∠J F J 31. Write a valid inequality of the restrictions on x. 0< x< 10 3 (5x – 10)° (2x)° For numbers 32 – 37, state the reason the following triangles are congruent. If they are not congruent, then state “not possible”. 32. 33. 34. HL SSS Not Possible 35. 36. 37. M is the midpoint of AB and CD. A C M Not Possible Not Possible SAS D B 38. State the missing sides or angles that we would need to have congruent, to prove the triangles congruent by the method indicated. A ∆AFE ≅ ∆BCD B By ASA: _∠FAE__ ≅ _∠CBD_ and _∠FEA_ ≅ _∠CDB_ By SAS: _∠FAE__ ≅ _∠CBD_ and _ AF _ ≅ _ BC _ OR F E D C By SAS: _∠AEF__ ≅ _∠BDC_ and _ FE _ ≅ _ DC _ For numbers 39 – 43, use the diagram to the right. R 1 39. If RI ≅ IT , what angles are congruent? ∠1 & ∠3 40. If TN ≅ IT , what angles are congruent? ∠11 & ∠8 2 I T 3 11 4 10 41. If ∠1 ≅ ∠6, what segments are congruent? RG & GH 8 G 42. The legs of isosceles ∆TNH are __ TN ____ and ___ NH ____ 5 9 7 N 6 H 43. The vertex angle of ∆RGH is ____G_____ 44. Solve for x and y. 45. Solve for x and y. x = 45 y = 135 x = 60 y = 120 x° y° x° y° 46. Solve for x and y. 47. Solve for x. y° x = 72 y = 36 (3x + 8)° x = 18 x° (2x + 20)° 72° 48. Solve for x. 49. Solve for x. (4x + 10)° x = 22.5 x = 33.25 40° 47° x° 50. Solve for x and y. x=9 y = 33 5x° (y + 12)° 51. Given: GH ≅ KL ∠G ≅ ∠K GI ≅ KJ Prove: HI ≅ LJ Statements 1. GH ≅ KL 2. ∠G ≅ ∠K 3. GI ≅ KJ 4. ∆HGI ≅ ∆LKJ 5. HI ≅ LJ Reasons 1. Given 2. Given 3. Given 4. SAS 5. CPCTC 52. Given: ∠MNP ≅ ∠OPN MN ≅ OP Prove: ∆MNP ≅ ∆OPN Statements 1. ∠MNP ≅ ∠OPN 2. MN ≅ OP 3. NP ≅ NP 4. ∆MNP ≅ ∆OPN Reasons 1. Given 2. Given 3. Reflexive Property 4. SAS 53. Given: ST || WV ST ≅ WV Prove: ∆TUS ≅ ∆VUW Statements Reasons 1. Given 1. ST ≅ WV 2. ST || WV 2. Given 3. ∠W ≅ ∠S 4. ∠T ≅ ∠V 5. ∆TUS ≅ ∆VUW 3. Alternate Interior Angles 4. Alternate Interior Angles 5. ASA G 54. Given: GJ is the altitude of HK HG ≅ KG Prove: ∆HGJ ≅ ∆KGJ H K J Statements Reasons 1. Given 1. GJ is the altitude of HK 2. ∠HJG and ∠KJG are right angles 3. ∆HJG and ∆KJG are right triangles 2. Definition of perpendicular 3. Definition of right triangle 4. Given 4. HG ≅ KG 5. JG ≅ JG 6. ∆HGJ ≅ ∆KGJ 55. Given: ∠1 ≅ ∠4 BF ≅ DC ∠5 ≅ ∠6 Prove: ∆ACD ≅ ∆EFB 5. Reflexive Property 6. HL C 5 D 3 4 E 1 B 2 A 6 F Statements 1. ∠1 ≅ ∠4 2. ∠1 is supp. to ∠2 3. ∠4 is supp. to ∠3 4. ∠2 ≅ ∠3 5. BF ≅ DC 6. ∠5 ≅ ∠6 7. ∆ACD ≅ ∆EFB Reasons 1. Given 2. Linear Pair Postulate 3. Linear Pair Postulate 4. Congruent Supplements Theorem 5. Given 6. Given 7. ASA 56. Given: ∠A ≅ ∠D AC ≅ DB Prove: SB ≅ SC S A B D C Statements 1. ∠A ≅ ∠D Reasons 1. Given 2. AS ≅ SD 3. AC ≅ DB 2. 3. Given 4. BC ≅ BC 4. Reflexive Property 5. AB ≅ DC 6. ∆SAB ≅ ∆SDC 5. Subtraction Property 6. SAS 7. CPCTC 7. SB ≅ SC 57. The perimeter of isosceles ∆RAM is greater than 28. Solve for x and determine which side is the base. x> R 10 3 RA is the base 8 A 2x + 3 x+7 M