Question

25. In the given figure, ABC is an isosceles triangle
in which AB = AC. E is a point on the side CB
produced such that EF is perpendicular to AC. If AD
is perpendicular to CB, prove that
AB X EF = AD X EC.​

Answer 1

Answer:

To prove : AB×EF=AD×EC

Proof :

AB=AC (given)

∴∠B=∠C (angles opposite to equal sides are equal) - (1)

In ΔABD and ΔECF

∠ABD=∠ECF    (from (1))

∠ADB=∠EFC  ( 90  )

therefore,

ΔADB is congruent to  ΔECF

AB×EF=AD×EC

∴ Hence proved.