# Angle Relationships Parallel Lines Worksheet

Angle Relationships Parallel Lines Worksheet
• Page 1
1.
$l$ || $m$ and $p$ is a transversal of $l$ and $m$. Use the figure to find the congruent interior angles.

 a. $\angle$4, $\angle$5 and $\angle$3, $\angle$6 b. $\angle$1, $\angle$8 and $\angle$2, $\angle$7 c. $\angle$4, $\angle$6 and $\angle$3, $\angle$5 d. $\angle$1, $\angle$7 and $\angle$2, $\angle$8

2.
Line $T$ is a transversal for the parallel lines $L$1 and $L$2. Use the figure to identify the special name for the angle pair $\angle$3 and $\angle$5.

 a. same-side interior angles b. congruent c. complementary d. corresponding angles

3.
Two parallel lines $L$1 and $L$2 are cut by a transversal $T$. Use the figure to identify the special name for the angle pair $\angle$2 and $\angle$6.

 a. corresponding angles b. alternate interior angles c. congruent angles d. supplementary angles

4.
Two parallel lines L1 and L2 are cut by a transversal T. Which of the following is true for the figure?

 a. $\angle$1 and $\angle$4 are supplementary. b. $\angle$1 and $\angle$4 are alternate interior angles. c. $\angle$1 and $\angle$4 are corresponding angles. d. $\angle$1 and $\angle$4 are vertical angles.

5.
L1 || L2 and T is a transversal of L1 and L2. Which of the following is true for the figure?

 a. $\angle$4 and $\angle$5 are congruent angles. b. $\angle$4 and $\angle$5 are alternate interior angles. c. $\angle$4 and $\angle$5 are supplementary angles. d. $\angle$4 and $\angle$5 are complementary angles

6.
State the postulate or theorem you would use, to prove that lines $m$ and $n$ are parallel.

 a. converse of corresponding angles postulate b. same - side exterior angles theorem c. converse of alternate interior angles theorem d. converse of same - side interior angles theorem

7.
Which theorem would you use to show that $a$ || $b$?

 a. corresponding angles theorem b. alternate interior angles theorem c. same-side interior angle theorem d. in a plane, if two lines are perpendicular to the same line, then they are parallel to each other.

8.
Select the correct statement(s)
I. If $m$$\angle$1 = $m$$\angle$6 and $r$ || $s$, then $m$$\angle$1 = 90
II. $r$ need not be parallel to $s$ even if $m$ $\angle$1 = $m$$\angle$6
III. If $m$$\angle$2 = $m$$\angle$8, then $r$ || $s$.

 a. I only b. II only c. I, II, and III d. III only

9.
If $\stackrel{‾}{\mathrm{AB}}$ || $\stackrel{‾}{\mathrm{CD}}$, $\stackrel{‾}{\mathrm{PR}}$ || $\stackrel{‾}{\mathrm{QS}}$, $m$$\angle$CQP = $x$ and $m$$\angle$SQD = $y$, then find $m$$\angle$EPR.

 a. $x$ - $y$ b. 180 - ($x$ + 2 $y$) c. 180 - ($x$ + $y$) d. 2$x$ + $y$

The lines $p$ and $q$ are parallel. Find the values of $x$ and $y$ in the figure shown.
 a. $x$ = 20 and $y$ = 60 b. $x$ = 32 and $y$ = 20 c. $x$ = 16 and $y$ = 20 d. $x$ = 16 and $y$ = 80