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

Solution:

Given: AB = AC

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

(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.

☛ Check: NCERT Solutions for Class 9 Maths Chapter 7

Video Solution:

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

NCERT Maths Solutions Class 9 Chapter 7 Exercise 7.3 Question 2

Summary:

If AD is an altitude of an isosceles triangle ABC in which AB = AC, then AD bisects BC and AD bisects ∠A.

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