Download 1 Name____________________________________________

Name____________________________________________ Review Date_______________
𝑙
1 2
5 6
9 10
13 14
𝑚
3 4
7 8
12
11
16
15
𝑙
1 2
5 6
𝑛
𝑝
9 10
13 14
𝑚
3 4
7 8
12
11
16
15
𝑛
𝑝
1. Name all the congruent corresponding angles in the figure above (hint, can I slide them down?)
2. Name all the congruent alternate interior angles in the figure above (hint, can I form a Z? Vertices
are alternate interior angles)
3. Name all the congruent alternate exterior angles in the figure above (hint – above and below the Z
vertices).
4. Name all the consecutive same side angles that are supplementary in the figure above (hint, can I
form a
)
5. Given 𝑙 ∥ 𝑚, 𝑚∠9 = (2𝑥2 + 10)°, and 𝑚∠16 = (6𝑥2 − 2𝑥 − 2)°, find the all possible values of 𝑥.
1
6.
Proof: Given m∠AEB= (3𝑥 + 17)°, m∠BEC= (𝑥 − 9)°.
m∠AED= 100°
Prove: Find 𝑥
Equation
Reason
A. m∠AEB= (3𝑥 + 17)°,
m∠BEC
m∠AED= 100°
B. m∠CED= (𝑥 − 9)°
C. m∠AED= m∠AEB + m∠BEC + m∠CED
D.
E.
Combine like terms
F.
G.
H.
2
7. Use the figure below and the given statements to complete the proof.
Given: 𝑎 ∥ 𝑏, 𝑐 ∥ 𝑑
Prove: ∠1 ≅ ∠3
𝑎
1
𝑏
2
3
𝑐
Statements
𝑑
Reasons
8. The measure of ∠𝐺𝐻𝐽 = 145°.
What does the diagram tell you about ∠𝐺𝐻𝐾 and ∠𝐾𝐻𝐿 ? What is the value of 𝑥, m∠𝐺𝐻𝐾,
𝑚∠𝐾𝐻𝐿, 𝑚∠𝐿𝐻𝐽, 𝑎𝑛𝑑 𝑚∠𝐺𝐻𝐽?
(5 points)
3
•
9. Create the converse and if they are both true, create the biconditional statement “If a polygon has
three sides then it is a triangle”
Converse: ______________________________________________________________
Biconditional: ____________________________________________________________
10. You can represent the measures of an angle and its complement as x° and (90 − x)°. Similarly, you
can represent the measures of an angle and its supplement as x° and (180 − x)°.
Use these expressions to find the measures of the angles described.
The measure of an angle increased by 44° is equal to the measure of its complement.
The measure of the angle is
is
° and the measure of its complement
°.
4
11. Proof
5
12. II In the diagram of a gate, the horizontal bars are parallel and the vertical bars are parallel.
Find x and y. Complete the explanation indicating which postulates and/or theorems were used
to find the values.
160°
(20x + 2y)°
70°
(5x + 2y)°
x=
y=
(20x + 2y)° =
(5x + 2y)° =
.
° by the
° by the
(select)
and
(select)
6