Download Review WS

Advanced Geometry
Topic 3 – Parallel & Perpendicular Lines
Review for TEST # 6 (3-1 to 3-5)
1.
Name: _____________________________________________________
Date: _________________________________ Period: ____________
a. Name a plane parallel to plane MNOP.
b. Name all segments skew to ̅̅̅̅̅
𝑀𝑅.
⃡ .
c. Name all lines parallel to 𝑀𝑃
Identify the transversal connecting each pair of angles. Then, classify the
relationship between each pair of angles as alternate interior, same-side
interior, corresponding, or alternate exterior.
2.
a. ∠10 and ∠16
d. ∠2 and ∠8
b. ∠3 and ∠11
e. ∠12 and ∠3
c. ∠6 and ∠16
f.
∠4 and ∠6
Find the values of x and y. Then find the measure of each labeled angle.
3.
4.
5.
6.
Given the following information, determine which lines, if any, are parallel.
State the postulate or theorem that justifies your answer.
7.
a. ∠6 ≅ ∠12
d. ∠10 ≅ ∠12
b. ∠2 ≅ ∠16
e. ∠2 ≅ ∠8
c. ∠3 ≅ ∠4
f.
∠6 and ∠7 are supplementary
Find the value of x, so that 𝓵 ∥ 𝒎. Then find the measure of each labeled angle.
8.
9.
10.
11.
Find the value of 𝒙 𝐰𝐡𝐞𝐧 𝓵 ∥ 𝒎. Then find the measure of each labeled angle.
12.
13.
(5𝑥 − 20)°
a, b, c, and d are distinct lines in the same plane. For each combination of relationships, tell how
a and d relate. Justify your answer.
14. a. 𝑎 ∥ 𝑏 ; 𝑏 ⊥ 𝑐 ; 𝑐 ∥ 𝑑
b. 𝑎 ∥ 𝑏 ; 𝑏 ∥ 𝑐 ; 𝑐 ⊥ 𝑑
c. 𝑎 ⊥ 𝑏 ; 𝑏 ∥ 𝑐 ; 𝑐 ⊥ 𝑑
15. Morris Avenue intersects both 1st Street and 3rd Street at right angles. 3rd Street is parallel to 5th Street.
How are 1st Street and 5th Street related? Explain.
Find the value of all variables. Then find the measure of each labeled angle.
16.
17.
18. The measure of one angle of a triangle is 108. The measures of the other two angles are in a ratio of
1 : 5. Find the unknown angle measures in the triangle.
Find the value of x. Then find the measure of each labeled angle.
19.
20.
VOCABULARY, POSTULATES, and THEOREMS to KNOW:
Lesson 3-1 Lines and Angles

Parallel lines

Parallel planes

Skew lines

Transversal

Alternate interior angles

Alternate exterior angles

Corresponding angles

Same-side interior angles
Lesson 3-2 Properties of Parallel Lines

Same-side interior angles postulate:
If 2 lines are parallel, then same-side interior angles are supplementary.

Alternate interior angles theorem:
If 2 lines are parallel, then alternate interior angles are congruent.

Corresponding angles theorem:
If 2 lines are parallel, then corresponding angles are congruent.

Alternate exterior angles theorem:
If 2 lines are parallel, then alternate exterior angles are congruent.
Lesson 3-3 Proving Lines Parallel

Converse of corresponding angles theorem:
If corresponding angles are congruent, then 2 lines are parallel.

Converse of alternate interior angles theorem:
If alternate interior angles are congruent, then 2 lines are parallel.

Converse of same-side interior angles postulate:
If same-side interior angles are supplementary, then 2 lines are parallel.

Converse of alternate exterior angles theorem:
If alternate exterior angles are congruent, then 2 lines are parallel.
Lesson 3-4 Parallel and Perpendicular Lines

In a plane, 2 lines parallel to the same line are also parallel.

In a plane, 2 lines perpendicular to the same line are also parallel.

Perpendicular transversal theorem:
In a plane, if a line is perpendicular to one of 2 parallel lines, then it is perpendicular to the other.
Lesson 3-5 Parallel Lines and Triangles

Exterior angle of a polygon

Remote interior angles

Triangle angle-sum theorem:
The sum of the measures of the angles of a triangle = 180°.

Triangle exterior angle theorem:
The measure of one exterior angle of a triangle is equal to the sum of its 2 remote interior angles.