Question

In an isosceles ∆ABC, the equal sides BA and CA are produced through A upto E and F respectively such that AE = AF. If K and L are the mid points of FB and EC, prove that FB = EC and AK = AL.



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Answer 1

Answer:

To prove : AB×EF=AD×EC

⇒ECAB=EFAD

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

⇒ECAB=EFAD

⇒AB×EF=AD×EC

∴ Hence proved.

Step-by-step explanation:

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