Question

a) ΔABC is an isosceles triangle such that AB = AC , AD ⊥BC .
b) Prove that ΔABD ≅ ΔACD.
c) Prove that ∠B = ∠C ?​

Answer 1

AB=AC (GIVEN)

ANGLE ADB= ANGLE ADC (90 DEGREE)

ANGLE ABD= ACD (angles opp to to equal sides in an isoceles triangle are also equal)

using AAS congruence rule triangle ABD=ACD

b=c (angles opp to equal sides are equal)

Answer 2

Answer:

△ABD and △ACD

AB=AC (given )

Then ∠ABD=∠ACD ( because AB=AC )

and ∠ADB=∠ADC=90( because AD⊥BC )

∴△ABD=△ACD

∠BAD=∠CAD

It is defective to use ∠ABD=∠ACD for proving this result