1 Pre-AP Geometry Chapter 5 Test Review Standards/Goals: C.1.f.: I can prove that two triangles are congruent by applying the SSS, SAS, ASA, and AAS congruence statements. C.1.g. I can use the principle that corresponding parts of congruent triangles are congruent to solve problems. D.2.a.: I can identify and classify triangles by their sides and angles. D.2.j. I can apply the Isosceles Theorem and its converse to triangles to solve mathematical and real-world problems. G.CO.8.: I can understand the idea of a rigid motion in the context of triangle congruence. Right Corollary Included Angles G.CO.10: I can prove theorems about triangles. IMPORTANT VOCABULARY Sum Theorem (Angle Sum Theorem) Scalene Isosceles Equilateral Equiangular Acute Vertex Exterior Angle Remote Interior Angles Exterior Angle Theorem Isosceles Base of a Legs of a Congruent CPCTC Theorem triangle triangle s Non-included SSS ASA SAS AAS sides/angles Obtuse Third Angle Theorem Included Sides This test will largely assess your ability to do the following: Identify pairs of triangles that are congruent to one another via the following postulates & theorems. Prove that two triangles are congruent using Geometry proofs #1. Use the following figure to do the following: a. Name the included side for <1 & <2. b. Name the included angle for sides AB & BC. #2. What are the missing coordinates of these triangles?
2 #3. ΔDEF is isosceles, <D is the vertex angle, DE = x + 7, DF = 3x 1, and EF = 2x + 5. Find x and the measures of EACH side of the triangle. ΔABF is isosceles, ΔCDF is equilateral, and the m<afd = 138. Find each measure. #1. m<cfd #2. m<afb #3. m<abf #4. m<cdf #5. m<dfe #6. m<fcd Find the measure of each angle in the figure below: #1. m<1 #2. m<2 #3. m<3 #4. m<4 #5. m<5 #6. m<6 Solve for x: #1. #2. #3. If ABC DEF, m<a = 40 and m<e = 54, what is m<c? #4. Suppose that ABC DEF, what concept could be used to prove that <3 = <4?
3 Proofs: #1. Given: <1 = <2; AK bisects <ZKC. Prove: ΔAKZ ΔAKC STATEMENTS #1. <1 = <2; AK bisects <ZKC #2. <3 = <4 #2. #3. AK = AK #3. #4. ΔAKZ ΔAKC #4. #2. Given: EG IA ; <EGA = <IAG Prove: <GEN <AIN STATEMENTS #1. EG IA ; <EGA = <IAG #2. AG = AG #2. #3. ΔGEA ΔAIG #3. #4. <GEN <AIN #4. #1. Given #1. Given REASONS REASONS #3. Given: C is the midpoint of BE; AC = CD Prove: ΔACB ΔDEC STATEMENTS REASONS #1. #1. Given C is the midpoint of BE; AC = CD #2. BC = CE #2. #3. <1 & <2 are vertical angles #3. #4. <1 = <2 #4. #5. ΔACB ΔDEC #5. #4. Given: <1 = <3 Prove: <6 = <4 STATEMENTS #1. <1 = <3 #1. Given #2. <1 & <4 are vertical angles; #2. <3 & <6 are vertical angles #3. <1 = <4; <3 = <6 #3. #4. <6 = <4 #4. REASONS
4 Short Answer Questions: Part I: Classify each triangle as: equilateral, isosceles, scalene, acute, equiangular, obtuse, or right. Some of the triangles may have more than ONE answer: Part II: State whether each pair of triangles are congruent or not. If so, state the postulate that justifies your answer. (SSS, ASA, AAS, SAS, or not possible).
5 Practice Multiple Choice: #1. C.1.f.: Given the diagram at the right, which of the following must be true? a. ΔXSF ΔXTG b. ΔSXF ΔGXT c. ΔFXS ΔXGT d. ΔFXS ΔGXT #2. C.1.g.: If ΔRST ΔXYZ, which of the following need not be true? a. <R = <X b. <T = <Z c. RT = XZ d. SR = YZ #3. C.1.g.: If ΔABC ΔDEF, m<a = 50, and m<e = 30, what is m<c? a. 30 b. 50 c. 100 d. 120 e. 160 #4. C.1.f.: What pair of angles can be proved congruent by SSS Postulate? #5. C.1.f.: Which pair of angles can be proved congruent by SAS Postulate?
6 #6. C.1.f.: Which pair of angles can be proved congruent by ASA Postulate? #7. C.1.f.: Which pair of angles can be proved congruent by AAS Theorem? #8. C.1.f.: In the figure at the right, the following is true: <ABD = <CDB and <DBC = <BDA. How can you justify that ΔABD ΔCDB? a. SAS b. SSS c. ASA d. CPCTC #9. C.1.f.: In the figure at the right, which theorem or postulate can you use to prove ΔADM ΔZMD? a. ASA b. SSS c. SAS d. AAS #10. C.1.g.: If ΔMLT ΔMNT, what is used to prove that <1 = <2? a. SAS b. CPCTC c. Definition of isosceles triangle d. Definition of perpendicular e. Definition of angle bisector #11. C.1.f.: In the figure at the right, which theorem or postulate can you prove ΔKGC ΔFHE? a. SSS b. SAS c. AAS d. ASA
Additional Practice of Congruence postulates: Is there enough information to prove that each pair of triangles are congruent or not? If so, state the postulate that you would use. 7
8 FLASHBACK SECTION: Solve each inequality, graph the solution and write an interval for its solution. #1. -10x > 70 #2. -2x 10 < 26 #3. 4 < 2x 2 18 #4. 2x 4 18 4 #5. -2 x + 5 + 10 > 22 #6. 10 + x + 9 < 8 #7. 4 8x 9 > 20 #8. x + 9 + 18 = 17 #9. 10 + x 12 = 7 #10. 2 x 10 #11. 2 x 10
9 #12. Evaluate each expression for the given values of the variables. a. 6c + 5d 4c 3d + 3c 6d; c = 4 and d = 2 b. 10a + 3b 5a + 4b + 1a + 5b; a = 3 and b = 5 c. 3m + 9n + 6m 7n 4m + 2n; m = 6 and n = 4 #13. What is the equation, in standard form, of the line that passes through (10, -6) and has a slope of ½? #14. What is the equation, in standard form, of the line that passes through (8, -2) and has a slope of 8? #15. Solve by any method you choose: { x + 2y = 7 2x y = 1
10 #16. True/False. Explain false. Refer to the figure below to answer the following equations: #1. The system of equations shown below would have one solution and it would be (0, -2) 3x y = 2 y = -x 2 #2. The system of equations shown below would have one solution and it would be (0, 2) y = -x - 2 x + y = 0 #3. The system of equations shown below would have one solution and it would be (2, 0) y = - x 2 3x 3y = -6 Short Answer Refer to the figure below and determine whether each pair of equations has NO SOLUTION, INFINITELY MANY SOLUTIONS or ONE SOLUTION. #1. x 2y = -3 4x + y = 6 ANSWER: #2. x + y = 3 x + y = 0 ANSWER: #3. y = -x 4x + y = 6 ANSWER: #4. x + y = 0 y = -x ANSWER: