Question

The sides BA and CA have been produced such that BA =AD & CA = AE .Prove that DE || BC.


please solve with process

Answer 1

Given: triangle ABC in which sides BA and CA are produced to D and E respectively, such that BA = AD and CA = AE

To prove: DE || BC
Construction: ED is joined
Proof: In triangles AED and BAC
CA = AE [given]
BA = AD [given]
angle EAD = angle BAC
therefore,
triangle AED is congruent to triangle BAC by SAS axiom

=> angle DEA = angle ACB
=> angle DEC = angle ECB
therefore ED || BC [Alternate angles are equal]
hence proved

Answer 2

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