Question

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

Answer 1

Step-by-step explanation:

In ABC,

Construction - Let AD is altitude of triangle ABC. intersecting BC.

AB = AC (given)

so It's an isosceles triangle in which two sides are equal, and two angles respective to equal sides are equal.

SO,

AB = AC ( given)

angle ABC = angle ACB. ( by property of isosceles )

AD = AD ( common)

=> By SSA congruence,

ABD =~ ACD

=> BD = CD

AND,

We know,

BC = BD + CD = BD + BD = 2BD

=> BD = BC/2

=> AD bisects side BC

=> AD is median.