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In the figure, p || q and r || s. Match each pair of congruent angles with the reason for their congruency.
Linear Pair Theorem
∠13 ≅ ∠16
corresponding angles for parallel lines p and q cut by the transversal r
∠1 ≅ ∠5
corresponding angles for parallel lines r and s cut by the transversal q
corresponding angles for parallel lines p and q cut by the transversal s
Vertical Angles Theorem
∠5 ≅ ∠13
∠10 ≅ ∠14

Congruent angles within two parallel lines are either vertical angles or corresponding angles. The reason for the congruence of the given angles are:

[tex]\angle 13[/tex] and [tex]\angle 16[/tex]

Reason: vertical angle theorem

[tex]\angle 1[/tex] and [tex]\angle 5[/tex]

Reason: corresponding angles for parallel lines p and q, cut by transversal r

[tex]\angle 5[/tex] and [tex]\angle 13[/tex]

Reason: corresponding angles for parallel lines r and s, cut by transversal q

[tex]\angle 10[/tex] and [tex]\angle 14[/tex]

Reason: corresponding angles for parallel lines p and q, cut by transversal s

From the given figure, we have the following:

Line p || Line q --- > This means that lines p and q are parallel

Line r || Line s --- > This means that lines r and s are parallel

From the attached figure, [tex]\angle 13[/tex] and [tex]\angle 16[/tex] are vertical angles.

Vertical angle theorem states that vertical angles are congruent.

So, the reason for the congruence of [tex]\angle 13[/tex] and [tex]\angle 16[/tex] is vertical angle theorem

[tex]\angle 1[/tex] and [tex]\angle 5[/tex] are corresponding angles of lines p and q, where line r passes through lines p and q.

Corresponding angles are congruent.

So, the reason for the congruence of [tex]\angle 1[/tex] and [tex]\angle 5[/tex] is that corresponding angles for parallel lines p and q, cut by transversal r

[tex]\angle 5[/tex] and [tex]\angle 13[/tex] are corresponding angles of lines r and s, where line q passes through lines r and s

So, the reason for the congruence of [tex]\angle 5[/tex] and [tex]\angle 13[/tex] is that corresponding angles for parallel lines r and s, cut by transversal q

[tex]\angle 10[/tex] and [tex]\angle 14[/tex] are corresponding angles of lines p and q, where line s passes through lines p and q

So, the reason for the congruence of [tex]\angle 10[/tex] and [tex]\angle 14[/tex] is that corresponding angles for parallel lines p and q, cut by transversal s

Read more about vertical and corresponding angles at:

https://brainly.com/question/11594212