Mathematics
In the given figure, the sides BA and CA of △ABC have been produced to D and E such that BA = AD and CA = AE. Prove that, ED || BC.
Answer
In △ABC and △ADE,
⇒ AB = AD [Given]
⇒ AC = AE [Given]
⇒ ∠BAC = ∠EAD [Vertically opposite angles are equal]
∴ △ABC ≅ △ADE [By S.A.S axiom]
⇒ ∠ABC = ∠ADE [Corresponding parts of congruent triangles are equal.]
From figure,
∠ABC and ∠ADE are alternate angles and since they are equal.
∴ ED || BC
Hence, proved that ED || BC.
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