Question

PM is the altitude of an isosceles triangle PQR in which PQ=PR.Show that PM bisects QR and PM bisects angle P​

Answer 1

Step-by-step explanation:

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

Answer:

Step-by-step explanation:

In triangle PQR,

ΔPQM and ΔPRM

   PM = PM

   PQ = PR

so,∠Q=∠R

ΔPQM≅ΔPRM

hence, QM=RM and ∠QPM = RPM [CPCT]