Question

In ∆PQR, PQ = PR. Prove that the perpendiculars from the mid-point of QR to PQ and PR
are equal.

Answer 1

Answer:

Step-by-step explanation:

PQR is an isosceles triangle with PQ = PR and M is the midpoint of QR. How do you prove that the line PM bisects <QPR?

We have two triangles PQM and PRM.

PQ = PR [given]

QM = MR [M being the midpoint of QR]

PM is common to both.

Hence the two triangles PQM and PRM are congruent [By SSS postulate]

Therefore <QPM = <RPM [ angles opposite equal sides QM and MR], so PM bisects the <QPR.