Question

a d is an attitude of an isosceles triangle ABC in which ab=AC show that​

AD bisects bc

Answer 1

Answer:

Given: AB = AC

Let's construct an isosceles triangle ABC in which AB = AC as shown below.

AD is an altitude of an isosceles triangle ABC in which AB = AC. Show that (i) AD bisects BC (ii) AD bisects ∠A

(i) In ΔBAD and ΔCAD,

∠ADB = ∠ADC (Each 90° as AD is an altitude)

AB = AC (Given)

AD = AD (Common)

∴ ΔBAD ≅ ΔCAD (By RHS Congruence rule)

∴ BD = CD (By CPCT)

Hence, AD bisects BC.

(ii) Since, ΔBAD ≅ ΔCAD

By CPCT, ∠BAD = ∠CAD

Hence, AD bisects ∠A.