Question

if AB = AC and angle B A D = angle C A E then prove that triangle ADE is an isosceles triangle

Answer 1

Heyy Mate, here is ur answer

Given:- Δ ABC is isosceles

AB = AC

BE=CD

To Prove :- AD= AE

Proof:- Since

AB =AC

therefore, angle C =angle. B(Angles Opposite to equal sides are equal)

In Δ ACD and Δ ABE

AC =AB (Given)

angle C = angle B (1 statement)

CD =BE ........(given)

Δ ACD congruent Δ ABE (C. P. C. T)

hence proved....

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Answer 2

Step-by-step explanation:

given : AB = AC

angle BAD = angle CAE

to prove : AD = AE

proof : angle BAD = angle CAE

AB = AC

angle B = angle C ( AB = AC, angles opposite to equal sides are also equal )

therefore Δ ABD congruent to Δ ACE by ASA

AD = AE ( by CPCT )

Hence proved that Δ ADE is an isosceles triangle.

Hope it helps you