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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 Triangle 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.

G.CO.10: I can prove theorems about triangles.

IMPORTANT VOCABULARY Triangle Triangle Sum Theorem

(Angle Sum Theorem) Scalene Triangle

Isosceles Triangle

Equilateral Triangle

Equiangular Triangle

Obtuse Triangle

Right Triangle

Acute Triangle Vertex Exterior Angle

Remote Interior Angles

Exterior Angle Theorem

Third Angle Theorem

Corollary Isosceles Triangle Theorem

Base of a triangle

Legs of a triangle

Congruent Triangles

CPCTC Included Sides

Included Angles

Non-included sides/angles

SSS ASA SAS AAS

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?

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#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?

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Proofs: #1. Given: <1 = <2; ̅̅ ̅̅ bisects <ZKC.

Prove: ΔAKZ ≌ ΔAKC

STATEMENTS REASONS

#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 REASONS

#1. ̅̅̅̅ ≌ ̅̅̅; <EGA = <IAG #1. Given

#2. AG = AG #2.

#3. ΔGEA ≌ ΔAIG #3.

#4. <GEN ≌ <AIN #4.

#3. Given: C is the midpoint of BE; AC = CD Prove: ΔACB ≅ ΔDEC

STATEMENTS REASONS

#1. C is the midpoint of BE; AC = CD

#1. Given

#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 REASONS

#1. <1 = <3 #1. Given

#2. <1 & <4 are vertical angles; <3 & <6 are vertical angles

#2.

#3. <1 = <4; <3 = <6 #3.

#4. <6 = <4 #4.

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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).

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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 ΔCDB?

a. SAS b. SSS c. ASA d. CPCTC

#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

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#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

3. ________________________

4. <LMP = <SMQ 4. ________________________

5. 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

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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.

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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. | |

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#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)

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#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: __________________________________