Question

In the figure,(p)parallel(q) and (r)pparallel(s). Match each pair of congruent angles with the reason for their congruency.

Answer 1

Corresponding angles for parallel lines r and s cut by transversal q. Corresponding angles are congruent angles. 
1 and 9
2 and 10
3 and 11
4 and 12

Corresponding angles for parallel lines p and q cut by transversal s. Corresponding angles are congruent angles. 
11 and 15
9 and 13
12 and 16
10 and 14

Corresponding angles for parallel lines p and q cut by transversal r. Corresponding angles are congruent angles. 
1 and 5
3 and 7
2 and 6
4 and 8

Linear pair theorem. These 2 angles are equal to 180°
∠1 + ∠2 = 180
∠3 + ∠4 = 180
∠9 + ∠10 = 180
∠11 + ∠12 = 180
∠5 + ∠6 = 180
∠7 + ∠8 = 180
∠13 + ∠14 = 180
∠15 + ∠16 = 180
∠1 + ∠3 = 180
∠2 + ∠4 = 180
∠9 + ∠11 =180
∠10 + ∠12 = 180
∠5 + ∠7 = 180
∠6 + ∠8 = 180
∠13 + ∠15 = 180
∠14 + ∠16 = 180

Vertical angles theorem. Vertical angles are congruent.
1 and 4
2 and 3
9 and 12 
10 and 11
5 and 8
6 and 7
13 and 16
14 and 15

Answer 2

Answer:

∠1≅∠5 by Corresponding angles for parallel line p and q cut by traversal r

∠5≅∠13 by Corresponding angles for parallel line r and s cut by traversal q

∠10≅∠14 by Corresponding angles for parallel line p and q cut by traversal s

∠13≅∠16 by Vertical angles theorem