Question

How are these triangles congruent?

Answer 1

`\triangle PTY \cong \triangle PSQ` by ASA

Explanation:

In triangle PTU and triangle PSQ

`\overline{PT} \cong \overline{PS}` [Side] [Given]

`\angle PTU \cong \angle PSQ` [Angle]

Vertical angles are those angles which are opposite to each other.

`\angle TPU \cong \angle SPQ` {Angle]

ASA(Angle-Side-Angle) postulates states if two angles and one included side of one triangle are congruent to two angles and the included side of the other triangle, then these triangle are congruent.

by ASA postulates;

`\triangle PTY \cong \triangle PSQ`