Question

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

Answer 1

Step-by-step explanation:

AB = AC ( isosceles triangle)

angle ABD = angle ACE ( In an isosceles triangle, base angles are equal)

BE = CD. if we remove DE from both BE and CD, then, BD = CE

{ explanation : BE = CD, then, BE - DE = CD - DE. so, BD = CE}

now,

AB = AC

angle ABD = angle ACE

BD = CE

so, ABD is congruent to ACE ( by side angle side criteria)

Therefore, AD = AE (corresponding parts of congruent triangles)

hence proved.