Question

7. Using Theorem 2.1, prove that a line drawn through the mid-point of one side of a triangle parallel to another side bisects the third side. (Recall that you have proved it in Class IX).​

Answer 1

Answer:

Theorem 6.1: If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, the other two sides are divided in the same ratio.

Step-by-step explanation:

Given:

In △ABC,D is midpoint of AB and DE is parallel to BC.

∴ AD=DB

To prove:

AE=EC

Proof:

Since, DE∥BC

∴ By Basic Proportionality Theorem,

DB

AD

=

EC

AE

Since, AD=DB

∴

EC

AE

=1

∴ AE=EC