Question

in the fig AD=1.5 cm DB=3cm AE=1 cm and EC=2cm. Show that DE ll BC​

Answer 1

Given:

• AD = 1.5 cm
• DB = 3 cm
• AE = 1 cm
• EC = 2 cm

To prove:

1. DE || BC

Method:

Let us first check if the sides are proportional

$\sf{\dfrac{AD}{DB}= \dfrac{AE}{EC}} \\\\\\:\implies \sf{\dfrac{1.5}{3} = \dfrac{1}{2}}\\\\\\:\implies \sf{\dfrac{1}{2} = \dfrac{1}{2}}$

Now we know that the sides are proportional.

By Converse of BPT,

DE || BC

Hence proved.

Additional Information:

1. Basic Proportionality Theorem (BPT) or Thales Theorem states that if a line is drawn parallel to a side of a triangle, then the other 2 sides are said to be divided in the same ratio i.e they are proportional.
2. Its converse states that if a line divides 2 sides of a triangle in a specific ratio, then the line is parallel to the third side.