Question

In an isosceles triangle ABC with AB=AD, D and E are points on BC such that BE=CD . Show that AD=AE

Answer 1

$\huge\boxed{\texttt{\color{yellow}{\fcolorbox{red}{blue} {SOLUTION}}}}$

Given :- A triangle ABC in which AB=AC. D and E are points on BC such that BE = CD.

To prove :- AD= AE.

proof :- BE=CD
= BE-DE = CD-DE
= BD = CE

NOW IN TRIANGLE ABD AND TRIANGLE ACE,

AB=AC
ANGLE B = ANGLE C
BD = CE

BY SAS CRITERIA, TRIANGLE ABD CONGRUENT TO TRIANGLE ACE.

BY CPCT, AD = AE

Hope that this answer will help you ❤️❤️

Answer 2

${\huge {\mathfrak {\orange {Answer :-}}}}$

Given that, AB = AC.

And ABC is an isosceles triangle.

So, angle B = angle C.

Now, given that,

BE = CD

Or, BE - DE = CD - DE

Or, BD = EC.

In ABD and ACE,

1. angle B = angle C.

2. AB = AC.

3. BD = EC.

Thus, they are congruent.

So, by C. P. C. T,

AD = AE.

➡️ $<b> Hence, proved that AD = AE. </b>$

That's it..