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

ln ΔABD and ΔCBE,

AB = BC                 ....(given)

AD ⊥ BC

CE ⊥ AB

To proved:

In ΔABD & ΔCBE

∠ ADB = ∠ CEB = 90°  ....[Perpendiculars]

∠B = ∠B                 ....(Common angle)

AB = BC

∴ ΔABD ≅ ΔCBE    ....(by AAS congruence)

⇒ AD = CE            ...(c.p.c.t.c)