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Alisiya [41]
3 years ago
9

Solve. Will Mark Brainliest.

Mathematics
1 answer:
Grace [21]3 years ago
3 0
<h3>Answer:</h3>
  1. Triangle ZXY is congruent to KXH according to AAS Congruency Postulate
  2. Triangle QPS is congruent to RPK according to AAS Congruency Postulate.

<h3>Proofs:</h3>

Both angles Y and H have the <em>same measurements</em>. Both angles ZXY and KXH have also the <em>same measurements</em>. And the <em>lengths</em> of both YX and HX are the <em>same</em>. 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 <em><u>sum</u></em> of the <em>measurements of the angles <u>QPR</u> and RPS</em> so as RPK is equal is equal to the <em><u>sum</u></em> of the measurements<em> of angles <u>SPK</u> and RPS</em><em> </em><em>and</em><em> </em><em>since</em><em> </em><em><u>QPR</u></em><em> </em><em>and</em><em> </em><em><u>SPK</u></em><em> </em><em>are</em><em> </em><em>have</em><em> </em><em>the</em><em> </em><em>same</em><em> </em><em>measur</em><em>ements</em><em>,</em><em> </em><em>they</em><em> </em><em>have</em><em> </em><em>the</em><em> </em><em>same</em><em> </em><em><u>sum</u></em>. 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.

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