Question

in an isoscales triangle ABC WITH AB=AC,D and E are points on BC such that BE = CD. prove that AD = AE​

Answer 1

Answer-

GIVEN A ΔABC in which AB=AC. D and E are point on BC such that BE=CD.

TO PROVE AD = AE.

PROOF BE=CD⇒BE−DE=CD−DE

⇒BD=CE.

Now, in ΔABDandΔACE, we have

AB=AC (given),

∠B=∠C [angles opposite to equal sides]

and BD=CE [proved above in (i)].

∴ ΔABD≅ΔACE (SAS-criteria).

Hence, AD=AE (c.p.c.t.).

Hope it helps :D