Mathematics
In a △ ABC, BD is the median to the side AC, BD is produced to E such that BD = DE. Prove that : AE is parallel to BC.
Triangles
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Answer
△ ABC with BD as median to the side AC and BD is produced to E such that BD = DE is shown below:
In △ ADE and △ BDC,
⇒ ∠ADE = ∠BDC (Vertically opposite angles are equal)
⇒ AD = DC (As BD is median to side AC)
⇒ BD = DE (Given)
∴ △ ADE ≅ △ BDC (By S.A.S. axiom).
We know that,
Corresponding parts of congruent triangles are equal.
∴ ∠EAD = ∠DCB
The above angles are alternate angles, since they are equal,
∴ AE || BC.
Hence, proved that AE is parallel to BC.
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