Question

In the following figure, show that triangle PSQ = triangle PSR​

Answer 1

Answer:

In triangle PSQ and triangle PSR

PQ = PR (GIVEN)

PS = PS (COMMON SIDE)

∠PSQ = ∠PSR (90°)

⇒ ∠PSQ ≅ ∠PSR

∴ Triangle PSQ = Triangle PSR

Answer 2

ΔPSQ = ΔPSR

GIVEN

PQS and PRS are triangle

PQ = PR = 6.5 cm

PS ⏊ QR

TO FIND

ΔPSQ = ΔPSR

SOLUTION

The above problem can be simply solved as follows;

In ΔPSQ and ΔPSR

PQ = PR (GIVEN)

∠PSQ = ∠PSR = 90° (Given)

PS = PS ( COMMON SIDE)

Therefore,

By Side - Angle - Side criterion

ΔPSQ ≈ ΔPSR

By CPCT

QS = SR

Therefore,

ΔPSQ = ΔPSR (Hence, proved)

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