Question

using basic proportionality theorem prove that the lines drawn through the points of trisection of one side of triangle parallel to another side trisect the third side.​

Answer 1

Given:

• In ΔABC, D is the midpoint of AB
• AD=DB.

To Prove:

• We have to prove that E is the mid point of AC.

Solution:

A line parallel to BC intersects AC at E

DE || BC.

Since, D is the mid-point of AB.

∴ AD=DB

$\leadsto$ AD/DB = 1 ....(i)

In ΔABC, DE || BC,

By using Basic Proportionality Theorem,

Therefore, ${\tt{ \dfrac{AD}{DB} = \dfrac{AE}{EC} }}$

From equation (i),

$\leadsto$ 1 = AE/EC

$\leadsto$ AE = EC

Hence Proved,

• E is the midpoint of AC.