Question

in the given figure base of the ΔABC IS EXTENDED to m and n where <ACN =<ABM prove<ABC=<ACB​

Answer 1

Answer:

REF.image

To prove : AB×EF=AD×EC

⇒

EC

AB

=

EF

AD

Proof :

AB=AC (∵ ABC is isosceles)

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

In ΔABD and ΔECF

∠ABD=∠ECF (from (1))

∠ADB=∠EFC (Both are 90

∘

)

Using AA similarity

ΔADB∼ΔECF

⇒

EC

AB

=

EF

AD

⇒AB×EF=AD×EC

∴ Hence proved.