Question

In ∆PQR , PQ=PR and PM is an altitude. Prove that PM bisects OPR as well as QR.​

Answer 1

Answer:

Given that, Δ PQR is an isosceles triangle where PQ=PR and PS is an altitude.

Now consider Δ PQS and ΔPRS

PQ = PS                        (Given)

∠PSQ=∠PSR                (Given Each 90° as PS is altitude)

PS = PS                         (Common)

Therefore,

Δ PQS ≅ ΔPRS            (R.H.S)

∴ ∠QPS=∠RPS              (C.P.C.T)

Hence, It gives the prove that  PS bisect ∠P .

Answer 2

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