# NCERT QUESTIONS ON TRIANGLE

1. Using basic proportionality theorem, prove that a line drawn through the mid point of one side of a triangle parallel to another side bisects the third side.

Proof: Let D is the mid point of AB and DE is parallel to BC.

To prove: E is the mid point of AC.

Proof: Since DE is parallel to BC, therefore by basic proportionality theorem $\frac{AB}{AD}=\frac{AC}{AE}$ $\frac{AB}{AD}-1=\frac{AC}{AE}-1$  $\Rightarrow$CA x CA = CB x CD

$\Rightarrow$CA2 = CB x CD proved

4. ABC is a right angled triangle, right angle at B and BD is perpendicular to AC. If AB = 6, BC = 8 and AC = 10, then BD = ?

Solution:

$\angle$C = $\angle$C

$\angle$B = $\angle$D

Hence $\triangle$ ABC is similar to BDC

Therefore, $\frac{AB}{BD}=\frac{AC}{CD}$ $\frac{6}{BD}=\frac{10}{6}$

So BD = 3.6

5. ABC is a triangle  in which DE is parallel to BC. If AD = 4, BD = 3, AE = 12, find the value of AC.

Solution: Since DE is parallel to BC, therefore  $\frac{AD}{BD}=\frac{AE}{CE}$ $\frac{4}{3}=\frac{12}{x}$

x = 9

so AC = 12 + 9 = 21