IMPORTANT VOCABULARY. Scalene Triangle. Triangle. SSS ASA SAS AAS sides/angles

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1 1 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 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, m<a = 40 and m<e = 54, what is m<c? #4. Suppose that, what concept could be used to prove that <3 = <4?

3 3 Proofs: #1. Given: <1 = <2; bisects <ZKC. Prove: ΔAKZ ΔAKC STATEMENTS #1. <1 = <2; bisects <ZKC #1. Given #2. <3 = <4 #2. #3. AK = AK #3. #4. ΔAKZ ΔAKC #4. #2. Given: ; <EGA = <IAG Prove: <GEN <AIN STATEMENTS #1. ; <EGA = <IAG #1. Given #2. AG = AG #2. #3. ΔGEA ΔAIG #3. #4. <GEN <AIN #4. 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 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 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.: In the figure at the right, the following is true: <ABD = <CDB and <DBC = <BDA. How can you justify that ΔABD a. SAS b. SSS c. ASA d. CPCTC ΔCDB? #5. 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 #6. 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

6 6 #7. 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 Refer to the proof/figure below in order to complete the proof: Given: M is the midpoint of LS; PM = QM Prove: ΔLMP ΔSMQ STATEMENTS REASONS 1. M is the midpoint of LS 1. Given 2. LM = MS 2. Definition of Midpoint 3. <LMP & <SMQ are vertical angles <LMP = <SMQ ΔLMP ΔSMQ 5. #8. C.1.f./G.CO.10.: Which of the following is the reason for STEP #3 in the proof? a. Definition of Linear Pair b. Vertical Angle Theorem c. Definition of Vertical Angles d. Vertical Angle Postulate #9. C.1.f./ G.CO.10: Which of the following is the reason for STEP #4 in the proof? a. Definition of Linear Pair b. Vertical Angle Theorem c. Definition of Vertical Angles d. Vertical Angle Postulate #10. C.1.f./ G.CO.10: Which of the following is the reason for STEP #5 in the proof? a. SSS b. ASA c. AAS d. SAS e. CPCTC

7 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 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. #5. -2 #6. #7. #8. #9. #10. #11.

9 9 #12. What is the equation, in standard form, of the line that passes through (10, -6) and has a slope of ½? #13. 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: { PRACTICE MULTIPLE CHOICE: #16. (D.1.g: ): What is the solution, (x, y), to this system of equations? a. (8, -3) b. (-6, -4) c. (-16/7, -15/7) d. (-8, -5) {

10 10 #17. 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: