Question

AD is an altitude of an isosceles triangle ABC in which AB = AC. Show that AD is also the
median of the triangle.​

Answer 1

Step-by-step explanation:

Draw the diagram of the triangle yourself. I am providing only the theory.

In triangle ABD and triangle ACD,

AB = AC (given)

angle ADB = angle ADC = 90°

(AD is an altitude to BC)

AD = AD (common)

Therefore,

triangle ABD ~=~ triangle ACD

(by SAS congruency)

So,

BD = CD ( by CPCT)

Therefore, AD is a median which divides BC into two equal parts