Question

The line drawn through the mid-point of one side of a triangle, parallel to another side bisects the third side. prove it

by proving the congruency of triangle AEF and CDF​

Answer 1

Step-by-step explanation:

in attachment ................

Answer 2

Statement:

The line drawn through the mid-point of one side of a triangle parallel to the base of a triangle bisects the third side of the triangle.

Proof of Converse Of The Mid Point Therom:

Given: In triangle PQR, S is the mid-point of PQ and ST ∥ QR

To Prove: T is the mid-point of PR.

Construction: Draw a line through R parallel to PQ and extend ST to U.

Proof: ST ∥ QR(given)

So, SU ∥ QR

PQ∥ RU (construction)

Therefore, SURQ is a parallelogram.

SQ = RU (Opposite sides of parallelogram)

But SQ = PS (S is the mid-point of PQ)

Therefore, RU = PS

In △PST and △RUT

∠1 =∠2 (vertically opposite angles)

∠3 =∠4 (alternate angles)

PS = RU (proved above)

△PST ≅ △RUT (by AAS criteria)

Therefore, PT = RT

T is the mid-point of PR.