Question

In a ΔABC,BD is the median to the side AC , BD is produce to E such that BD = DE
Prove that AE is parallel to BC.​

Answer 1

Answer:

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Step-by-step explanation:

Given: △ABC, BD is median on AC. BD produced to E BD=DE.

To prove: AE∥BC

In △AED and △BDC,

∠ADE=∠BDC (Vertically opposite angles)

AD=DC (D is mid point of AC)

BD=DE (Given)

Hence, △AED≅△BEC (SAS rule)

Thus, ∠DAE=∠DCB (By cpct)

but these are alternate angles w.r.t. AE and BC. Hence, AE∥BC