Question

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

Answer 1

AD = AE

Explanation:

Given: ∆ABC is an isosceles triangle with AB = AC.

D and E are points on BC such that BE = CD.

To prove: AD = AE

Proof:  

In ∆ABE and ∆ADC, AB = AC and BE = CD. (Given)

Since ∆ABC is an isosceles triangle, <B = <C (Base angles of an isosceles triangle).

Two sides are equal and one angle is equal.

So  ∆ABE is congruent to ∆ADC.

Hence the corresponding sides of the two triangles will be equal.

So AD = AE. Hence proved.