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In the Given Figure Prove That: (I) Pq = Rs (Ii) Ps = Qr - Mathematics

Sum

In the given figure prove that:
(i) PQ = RS
(ii) PS = QR

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Solution

Proof:
In Δ PQR and Δ PSR,
PR = PR ..........(common)
∠PRQ = ∠RPS ............(given)
∠PQR = ∠PSR .......(given)
∴ Δ PQR ≅ Δ PSR .................(A.A.S. Axiom)
Hence

(i) PQ = RS .............(c.p.c.t.)

(ii) QR = PS ...............(c.p.c.t.)
or PS = QR
Hence proved.

Concept: Extend Congruence to Simple Geometrical Shapes E.G. Triangles, Circles.
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APPEARS IN

Selina Concise Mathematics Class 7 ICSE
Chapter 19 Congruency: Congruent Triangles
Exercise 19 | Q 9
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