Question

in figure prove that AD=BE if angle A=angle B and DE ll AB​

Answer 1

We hve given AD=BE and angle A =B and DE || AB. Similarly AD=BE because points ADBE lies in same parallelogram and A and B angles are stand on a sane base

Answer 2

Answer:

Given : In ∆ ABC DE II AB and ∠A = ∠B → ∠CAB = ∠CBA

To Prove : AD = BE

Proof :

since, DE II AB ( GIVEN)

therefore ∠CDE = ∠CAB ----------------(1)

∠CED = ∠CBA ----------------(2)

From (1) and (2),

∠CDE = ∠CED

Therefore in ∆CDE

DC = EC  [Sides opposite to equal angles are equal]

Now since, DE II AB

therefore by Basic Proportionality Theorem

AD/DC = BE/EC

→  AD/EC = BE/EC     [Since DC = EC]

→ AD = BE

HENCE PROVED