Question

Prove that any line segment drawn from the vertex of a triangle to the base is bisected by the line
segment joining the midpoints of the other sides of the triangle.​

Answer 1

Given :

E and F are mid points on side AB and AC of triangle respectively. AL is line segment drawn from A to BC.

To Prove :

AM = LM

Proof :

By theorem we know that,

Line joining mid points of triangle are always parallel and half to that of base.

Therefore, EF || BC

In ∆ABL and ∆ACL,

That's why, EM || BL and MF || LC

Here, E is mid point on AB and F is mid point on AC.

Hence by theorem mentioned above,

Point M is mid point on line segment AL.

Hence, AL = LM