Question

(a)

Parallel lines, and I are intersected by transversal m, forming angles 1 to 8, as shown in the diagram.
m
1
2
5
6
3
a. Identify all of the pairs of alternate interior angles.
Pair 1:
22 and 2
Pair 2:
23 and 2
b. Use rigid motion to explain why alternate interior angles are equal in measure.

Answer 1

(a) 7 and 6

(b) The alternate interior angles can be mapped onto each other using a reflection and a rotation, both of which are rigid motions. Rigid motions preserve congruency, meaning the alternate interior angles are congruent. By the definition of congruent angles, the alternate interior angles are equal in measure.