Question

In a triangle, ABC, AB = BC, AD is perpendicular to side BC and CE is perpendicular to side AB. Prove that: AD = CE.

Answer 1

In ΔABD and ΔCBE,
AB = BC                        ( given )
∠ADC =∠CEB = 90⁰ 
∠B =∠B                        ( common angel )
∴ ΔABD≅ΔCBE            ( by SAS congruence  )
⇒ AD =CE                   ( c.p.c.t  )