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 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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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 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 ∆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?
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Proofs: #1. Given: <1 = <2; AK̅̅ ̅̅ bisects <ZKC.
Prove: ΔAKZ ≌ ΔAKC
STATEMENTS REASONS
#1. <1 = <2; 𝐴𝐾̅̅ ̅̅ bisects <ZKC #1. Given
#2. <3 = <4 #2.
#3. AK = AK #3.
#4. ΔAKZ ≌ ΔAKC #4.
#2. Given: EG̅̅̅̅ ≌ IA̅̅̅; <EGA = <IAG Prove: <GEN ≌ <AIN
STATEMENTS REASONS
#1. EG̅̅̅̅ ≌ IA̅̅̅; <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.: 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?
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#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
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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. |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
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#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 = 72𝑥 − 𝑦 = −1
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#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: __________________________________
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