Download 1st Semester Final Review Packet

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: ∠𝐵 ≅ ∠𝐷 and ̅̅̅̅
𝐴𝐵 ≅ ̅̅̅̅
𝐶𝐷
̅̅̅̅̅ ≅ 𝐶𝑀
̅̅̅̅̅
Prove: 𝐴𝑀
2. Given: ∠1 ≅ ∠5
Prove: ∠1 ≅ ∠7
(You may write a 2-column proof here or write out in words why this is true.)
3. Complete a proof.
Given: 𝑃𝑄𝑅𝑆 is a parallelogram
̅̅̅̅ ≅ 𝑃𝑆
̅̅̅̅
Prove: 𝑄𝑅
YOU MAY NOT USE THE PROPERTIES OF A PARALLELOGRAM
in this proof- only the DEFINITION OF A PARALLELOGRAM!!
4. Complete a proof.
Given: ̅̅̅̅̅
𝑀𝑄 ∥ ̅̅̅̅
𝑂𝑃
Prove: ∆𝑀𝑁𝑄~∆𝑃𝑁𝑂
5. Complete a proof.
̅̅̅̅
Given: ̅̅̅̅
𝐷𝐸 ∥ 𝐵𝐶
Prove: ∆𝐴𝐵𝐶 ~ ∆𝐴𝐷𝐸
6. Use the diagram on the below.
A. Construct a perpendicular bisector (segment bisector) to ̅̅̅̅̅
𝑾𝒀.
B. Construct the angle bisector of ∠𝑊𝑌𝑋.
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. ⃗⃗⃗⃗⃗
𝑌𝑉 bisects ∠𝑋𝑌𝑍.
⃗⃗⃗⃗⃗⃗⃗
𝑌𝑊 bisects ∠𝑋𝑌𝑉. 𝑚∠𝑊𝑌𝑉 = 36. What is the 𝑚∠𝑋𝑌𝑉?
2. Based on the figure to the right, which congruence theorem justifies the final
statement in a proof that ∆𝐴𝐸𝐺 ≅ ∆𝐶𝐸𝐹?
a. AA
b. AAS
c. ASA
d. SAS
e. SSS
3. Perform the following composition of transformations on ̅̅̅̅
𝐷𝐸 .
R < x-axis > ◦ 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
𝑙
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. ∠6 and ∠14 are corresponding angles
b. ∠5 and ∠4 are alternate exterior angles
c. ∠13 and ∠5 are consecutive/same side interior angles
d. ∠7 and ∠10 are alternate interior angles
e. ∠16 and ∠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.
⃗⃗⃗⃗⃗⃗ bisects ∠𝐶𝐵𝐴. Find the 𝑚∠𝐴𝐵𝐶.
𝐵𝐷
13. What value of 𝑥 makes 𝑚 ∥ 𝑛?
a. 20
b. 25
c. 38
d. 68
e. 83
(2𝑥 + 15)°
55°