Question

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Answer 1

Answer:

1. Triangle ZXY is congruent to KXH according to AAS Congruency Postulate
2. Triangle QPS is congruent to RPK according to AAS Congruency Postulate.

Proofs:

Both angles Y and H have the same measurements. Both angles ZXY and KXH have also the same measurements. And the lengths of both YX and HX are the same. Because of these, Triangles ZXY and KXH are congruent according to the Angle Angle Side Congruency Postulate. And because triangles ZXY and KXH are congruent, YZ and HK have the same lengths because they are the same sides of the same triangles.

Given that angles QPR and SPK have the same measurements, then angles QPS and RPK have also the same measurements because the measurement of QPS is equal to the sum of the measurements of the angles QPR and RPS so as RPK is equal is equal to the sum of the measurements of angles SPK and RPS and since QPR and SPK are have the same measurements, they have the same sum. Angle Q and PRK have the same measurements. PQ and PR have the same lengths. Because of these, Triangles QPS and RPK are congruent according to the Angle Angle Side Congruency Postulate. And because triangles QPS and RPK are congruent, PS and PK are congruent because they are the same sides of the same triangles.