Question

In a triangle ABC, AB=AC. Show that the altitude AD is a median also.

Answer 1

Given: ABC is an isosceles triangle(AB=AC)
AD is the altitude
To prove: AD is the median
Proof:
AB=AC (given)
AD is common
∠ADB=∠ADC=90° (AD is the height)
∴By RHS criteria, ΔABD is congruent to ΔACD

By CPCT,
BD=CD
And area of congruent triangles are equal.

A median from a vertex divides the opposite side into two halves and the two triangles formed are equal in area.

Hence AD is the median as well as height