Question

Someone please help me.

Answer 1

Explanation:

1. PQ║TS, PQ ≅ TS, PT and QS are transversals to the parallel lines . . . given

2. ∠P ≅ ∠T . . . alternate interior angles at PT

3. ∠Q ≅ ∠S . . . alternate interior angles at QS

4. ΔPQR ≅ ΔTSR . . . ASA postulate

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You can use any pair of angles together with the sides PQ and TS. If you use the vertical angles and one of ∠T or ∠S, then you must invoke the AAS postulate for congruence, as the side is not between the two angles.