Question

abc is an isosceles triangle in which altitudes bd and ce are drawn to equal sides ac and ab respectively .show that these altitudes are equal.​

Answer 1

Answer:

In triangle ABC, sides AB = AC

and BD is perpendicular to AC

CE is perpendicular to AB

from triangles ABD and ACE,

AB = AC (given)

angle A = angle A (common angle)

angle BDA = angle CEA (90°)

By AAS (or RHS) criterion, triangle ABD and ACE are congruent.

By CPCT, BD = CE

Answer 2

Answer:

Given: ΔABC is isosceles (AB = AC)

To Prove: BD and CE

Proof:-

Consider ΔBCE and ΔBCD

= BC = BC (Common Side)

= <BEC = <BDC = 90 (BD and CE are altitudes)

= <C = <B (AB = CD) and (ΔABC is an Isosceles)

∴ By SAS Congruence rule,

= ΔBCE ≅ ΔBCD (C.P.C.T)

= BC = CE (CPCT)