Question

In the following figure, ∠D = ∠E and `"AD"/"DB" = "AE"/"EC"`, Prove that ΔBAC is an isosceles triangle.

Answer 1

Given: ∠D = ∠E and `"AD"/"DB" = "AE"/"EC"`

To prove: ΔBAC is an isosceles triangle.

Proof: `"AD"/"DB" = "AE"/"EC"`

By converse of BPT, DE || BC

∴ ∠ADE = ∠ABC   ...(Corresponding angles)

And ∠AED = ∠ACB   ...(Corresponding angles)

∵ ∠ADE = ∠AED   ...(Given)

∴ ∠ABC = ∠ACB

So, BAC is an isosceles triangle.

Hence Proved.