**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
CA x CA = CB x CD

^{2}= 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: **

Hence ABC is similar to BDC

Therefore,

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

x = 9

so AC = 12 + 9 = 21