Question

IN FIGURE (iv) WHICH PAIRS OF TRIANGLES ARE CONGRUENT BY "SAS" { SIDE- ANGLE- SIDE } CONGRUENCE CONDITION ? IF CONGRUENT,WRITE THE CONGRUENCE OF THE TWO TRIANGLES IN SYMBOLIC FORM.​

Answer 1

Answer:

In ΔSPQ and ΔSRQ, we get,

PS = QR [Both are 4 cm]

∠SPQ = ∠SRQ [Both are 90°]

PQ = SR [Opposite sides of rectangle are

equal]

So, by SAS - congruency criteria, we get,

ΔSPQ ≅ ΔSRQ

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Answer 2

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We know By Pythagoras Theorm,

Hypotenuse² = Base² + Perpendicular²

So, QS² = PQ² + PS²

Also, QS² = RS² + QR²

On comparing both,

PQ² + PS² = RS² + QR²

PQ² + 4² = RS² + 4²

PQ² = RS²

so, PQ = RS

Now in ΔQPS and ΔSRQ,

PQ = RS ( Proved above)

angle QPS = angle QRS ( Both 90 )

QR = SP (Both 4cm)

Hence by SAS criterion,

ΔQPS ≅ ΔSRQ.

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