Question

Triangle pqr is an isosceles triangle and ps is altitude on the side of qr.Prove that triangle pqs is congurent to triangle prs

Answer 1

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Answer 2

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Question: ΔPQR is an isoceles triangle and PS is altitude on the side of QR. Prove that ΔPQS ≅ ΔPRS.

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Pre-requisite Knowledge

You must be familiar with concepts related to Congruency, such as

• SSS congruency
• SAS congruency
• ASA conruency
• AAS congruency
• RHS congruency

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Answer

Given,

PQ = QR

PS is an altitude to the side QR

To Prove,

ΔPQS ≅ ΔPRS.

Proof,

In  ΔPQS and ΔPRS.

PQ = PR (given)

PS = PS (common side)

∠PSQ = ∠PSR = 90° (Altitude)

∴  ΔPQS ≅ ΔPRS by RHS congruency

(*Remember* RHS cannot be used when we simply obtain an angle is equal to 90°, We must get a Hypotenuse, Altitude and an 90° angle to use RHS congruency)

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Hope It Helps!