Parallel Lines Review

In the diagram, lines a and b are parallel, but lines m and n are not. What is the value of x and y?

Type answer as x= ,y=

(no spaces)

Answer explanation

A = A

5x+42=8x-15

x=19

A+O=180

10+6y+4y+70=180

y=10

If $\angle14\cong\angle6$ , determine which lines, if any, must be parallel.

• p $\parallel$  q

• r $\parallel$  s

• p $\parallel$  q and r $\parallel$  s

• no lines are parallel

Answer explanation

If alternate interior angles are congruent, then the lines are parallel.

Given: a $\parallel$  c and d $\parallel$  e

Find the value of z.
Type the number to answer.

Answer explanation

Given m $\parallel$  n, which congruence statements are true?

Check all that apply.

•  $\angle14\cong\angle6$  

•  $\angle4\cong\angle7$  

•  $\angle1\cong\angle2$  

•  $\angle10\cong\angle3$  

•  $\angle12\cong\angle16$  

Answer explanation

angles 14 and 6 are NOT on lines m and n
angles 4 and 7 are congruent corresponding angles
angles 1 and 2 are vertical so always congruent
angles 10 and 3 are not on lines m and n
angles 12 and 16 are congruent alternate exterior angles

 $\angle12\ and\ \angle16$  

Which angle relationship describes the angle pair listed?

• corresponding

• same-side interior

• alternate interior

• alternate exterior

• same-side exterior

Answer explanation

alternate exterior angles are on different sides of the transversal and outside the lines

 $\angle2\ and\ \angle6$  

Which angle relationship describes the angle pair listed?

• corresponding

• same-side interior

• alternate interior

• alternate exterior

• same-side exterior

Answer explanation

alternate interior angles are on different sides of the transversal and inside the lines

 $\angle9\ and\ \angle8$  
Which angle relationship describes the angle pair listed?

• corresponding

• same-side interior

• alternate interior

• alternate exterior

• same-side exterior

Answer explanation

Same-side interior angles are on the same side of the transversal and inside the lines

 $\angle3\ and\ \angle1$  
Which angle relationship describes the angle pair listed?

• corresponding

• same-side interior

• alternate interior

• alternate exterior

• same-side exterior

Answer explanation

corresponding angles are on the same side of the transversal and in the same position

 $\angle4\ and\ \angle13$  
Which angle relationship describes the angle pair listed?

• corresponding

• same-side interior

• alternate interior

• alternate exterior

• same-side exterior

Answer explanation

same-side exterior angles are on the same side of the transversal and outside of the lines

Four lines and four congruent angles are identified in the diagram. Which statement must be true?

• only m $\parallel$ n

• only p $\parallel$ q

• p $\parallel$ q and m $\parallel$ n

• no pair of lines is parallel.

Answer explanation

intersections match from line m to line n
intersections do not match from line p to line q