Question

∆ DEF is an Isosceles triangle with DE = EF. If ˪F = 500 , Find the measure of ˪D and ˪E.​

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.