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1st Semester Final Review Packet 2016-17 Geometry Name__________________________________________ Date ____________________________Block__________ Part 1: Constructed Response 1. Complete a proof using the diagram to the right. Given: β π΅ β β π· and Μ Μ Μ Μ π΄π΅ β Μ Μ Μ Μ πΆπ· Μ Μ Μ Μ Μ β πΆπ Μ Μ Μ Μ Μ Prove: π΄π 2. Given: β 1 β β 5 Prove: β 1 β β 7 (You may write a 2-column proof here or write out in words why this is true.) 3. Complete a proof. Given: πππ π is a parallelogram Μ Μ Μ Μ β ππ Μ Μ Μ Μ Prove: ππ YOU MAY NOT USE THE PROPERTIES OF A PARALLELOGRAM in this proof- only the DEFINITION OF A PARALLELOGRAM!! 4. Complete a proof. Given: Μ Μ Μ Μ Μ ππ β₯ Μ Μ Μ Μ ππ Prove: βπππ~βπππ 5. Complete a proof. Μ Μ Μ Μ Given: Μ Μ Μ Μ π·πΈ β₯ π΅πΆ Prove: βπ΄π΅πΆ ~ βπ΄π·πΈ 6. Use the diagram on the below. A. Construct a perpendicular bisector (segment bisector) to Μ Μ Μ Μ Μ πΎπ. B. Construct the angle bisector of β πππ. W Y X 7. Write and solve an equation to help you answer the questions below, using the diagram provided. a. What is the value of x? b. What is the value of y? 8. Specify a series of transformations that map PDM onto EJS. You may use descriptions, function rules, and/or coordinate rules as long as they are complete. P D M J S E Part 2: Multiple Choice 1. Draw a picture that represents the following information, then answer the question. βββββ ππ bisects β πππ. βββββββ ππ bisects β πππ. πβ πππ = 36. What is the πβ πππ? 2. Based on the figure to the right, which congruence theorem justifies the final statement in a proof that βπ΄πΈπΊ β βπΆπΈπΉ? a. AA b. AAS c. ASA d. SAS e. SSS 3. Perform the following composition of transformations on Μ Μ Μ Μ π·πΈ . R < x-axis > β¦ r < 270, origin >. 4. Which of the following transformations will map ABDC onto EFHG? (Circle ALL that apply) a. Reflection over the x-axis b. Reflection over the y-axis c. Reflection over line l d. Rotation 180° about the origin π H F G E 5. Triangle XYZ is REFLECTED onto triangle PQR across line t. If line segments are drawn between each corresponding preimage and image point, what is true about the segments? (Circle ALL statements that are TRUE). Hint: Draw a picture to help you. A. The segments are congruent. B. The segments are bisected by the line of refection. C. The segments are parallel. D. The segments are perpendicular to the line of reflection. 6. Which of the following statements are false? (Cirlce ALL that apply) a. β 6 and β 14 are corresponding angles b. β 5 and β 4 are alternate exterior angles c. β 13 and β 5 are consecutive/same side interior angles d. β 7 and β 10 are alternate interior angles e. β 16 and β 1 are vertical angles 7. For the following pair of triangles, tell what other parts must be congruent in order to prove the triangles congruent for EACH shortcut. 8. Determine which pair of triangles are similar. (Circle ALL that apply)!! 9. Find the value of x. 10. Find the value of x. 2(x+6) 42o 11. Find the value of x in the parallelogram GEOM. 12. ββββββ bisects β πΆπ΅π΄. Find the πβ π΄π΅πΆ. π΅π· 13. What value of π₯ makes π β₯ π? a. 20 b. 25 c. 38 d. 68 e. 83 (2π₯ + 15)° 55°