Question

Given: S is the midpoint of QR, QR¯⊥PS¯ and ∠RSP and ∠QSP are right angles. Prove: PR≅PQ

Answer 1

ΔRSP ≅ ΔQSP by SAS. Therefore, PR ≅ PQ by CPCTC theorem.

What is the CPCTC Theorem?

If two triangles are congruent, the CPCTC theorem states that all corresponding parts of the two triangles would also be congruent to each other.

Since S is the midpoint of QR, therefore, RS ≅ QS (one pair of congruent sides)

∠RSP ≅ ∠QSP [right angles] (one pair of congruent included angles)

SP ≅ SP based on the reflexive property (one pair of congruent sides)

Therefore, ΔRSP ≅ ΔQSP by SAS.

Conclusively, PR ≅ PQ by CPCTC theorem.

Learn more about the CPCTC theorem on:

brainly.com/question/6076251

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