Math, asked by ASingh2040, 8 months ago

In the given figure the sides BA and CA have been produced such that BA=AD and CA=AE.Prove that the segment DE||side BC

Answers

Answered by probaudh
0

Given that,

the sides BA and CA have been produced such that BA= AD and CA=AE and given to prove DE|| BC

Consider triangle BAC and DAE,

We have BA = ADand CA = AE [∴ given in the data] And also ∠BAC =∠DAE [∴ vertically opposite angles] So, by SAS congruence criterion,

we have ΔBAC ≅ ΔDAE ⇒ BC = DE and ∠DEA=∠BCA,∠EDA=∠CBA [Corresponding parts of congruent triangles are equal]

Now, DE and BC are two lines intersected by a transversal DB such that ∠DEA=∠BCA, i.e., alternate angles are equal

Therefore, DE || BC

like and follow

marks of brainliest

Similar questions