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Unit 5H Test Name________________________Period_______ Read all of the questions carefully. All work must be shown under the appropriate problem to receive full credit. Label all diagrams and proofs appropriately. (2 points each unless specified) 60 pts total. 1ABC and DEF have the following properties: , and . Drawing is NTS. B E A If m a. b. C F D = 15, = 14, and m = 30 , and = (5n + 15)°, determine the value of n. 11 n=2 c. n= 3 n=3 d. n=9 2. In the triangles shown below, may be combined to map onto listed in order. Circle all that apply. , y A X B C Y x Z a. b. c. d. e. A reflection across the x-axis A reflection across the y-axis A reflection across the line A vertical translation A horizontal translation = n + 12, = 3n + 5, and , and . Which rigid motions below ? This requires a composition of transformations. They are For questions 3-4, consider ABC where AB = BC and mA 40 . 3. mB mC 140 (A) True (B) False 4. mC 100 (C) True (D) False 5. Given: ; and are right angles. Prove: Proof: Which justification belongs in Step 2? a. Isosceles Theorem b. Reflexive Property of Congruence c. Right Angles are Congruent Theorem d. CPCTC 6. In the figure, H is the midpoint of (A) (B) and SAS ASA . What reason can be used in a proof to show (C) Def. of bisector (D) CPCTC ? 7. and are altitudes to the congruent sides of isosceles triangle . W Q P X Y Keisha is going to prove by showing they are congruent parts of the congruent triangles and . By what congruence postulate is ? a. AAS - because triangle WXY is isosceles, its base angles are congruent. Perpendicular lines form right angles, which are congruent; and segment is shared. b. SSS - because segment would be parallel to segment . c. SSA - because segment is shared; segments and are altitudes, and WXY is isosceles, so base angles are congruent. d. ASA - because triangle WXY is isosceles, its base angles are congruent. Segment is shared; and perpendicular lines form right angles, which are congruent. 8. Which of the following statements can be concluded from the given triangle? S U a. b. c. d. e. f. g. h. T is an isosceles triangle. is an equilateral triangle. 9. Given: ASA. 10. , . State the congruence that is needed to prove using Which figure contains two triangles that are NOT congruent? a. c. d. b. For questions 11-13, consider a triangle ABC that has been transformed through rigid motions and its image compared to XYZ . Determine if the given information is sufficient to draw the provided conclusion. 11. e. Given A X B Y C Z (A) True (B) False Conclusion ABC XYZ Given A X B Y 12. Conclusion ABC XYZ BC YZ (A) True (B) False 13. Given A X Conclusion AB XY ABC XYZ BC YZ (A) True (B) False 14. Use the triangle. What is the value of x? 80 ° (A) 75 (B) 25 x° 4 x 25 (C) 21 (D) 15 15. In the isosceles triangle below, mH 124 . What is the measure of F ? (A) 28° H (B) 56° 124° (C) 124° (D) 180° G F 16. What term describes a transformation that does not change a figure’s size or shape? (A) Reflexive (C) Conguent (B) Dilation (D) Isometry 17. Find the coordinates of the other endpoint of the segment with the given endpoint A and midpoint M. 𝐴(−4, 3) and 𝑀(−2, −1) ______________ 18. Given A 2, 6 and B 4, 2 . What is the distance from A to B? ______________ 19. In the diagram, mABC 85 . What is the value of x? Grid your answer in the box. A 3 x 10 B D 2x C 20. Given that ∠1 ≅ ∠3, which lines must be parallel? 21. (3 points) Decide whether it is possible to prove that the triangles are congruent. If it is possible, tell which congruence postulate or theorem you would use and mark it correctly on the diagram. 22. and are congruent. y 5 L 4 3 2 K 1 J –5 –4 –3 –2 –1 –1 1 O 2 3 4 5 x –2 –3 N –4 M –5 Use correct mathematical notation to explain what transformation or transformations would map to 23. Which lines, if any, must be parallel based on the given diagram and information and WHY. Given 𝑚∠8 = 𝑚∠13. a 1 2 9 10 3 4 b 11 5 6 7 8 c 24. (4 points) Solve the equation and state a reason for each step: 2(𝑥 − 1) + 3 = 17 12 13 14 15 16 d ? 25. In the diagram, NK LM and 1 2 . Prove LMK NKM . (3 points) L 1 K ⃡ is the perpendicular bisector of AB . (6 points) 26. In the diagram, 𝐷𝐶 D A C B Prove ̅̅̅̅ 𝐷𝐴 ≅ ̅̅̅̅ 𝐷𝐵. N 2 M