**CBSE NCERT Solutions Chapter 6 Triangles Exercise 6.4 Question 3**

**3. **ABC and DBC are two triangles on the same base BC. If, AD intersects BC at O, show that .

**Solution:**

**Construction: **Draw perpendicular AE from point A to side BC and draw perpendicular DF to side BC.

Area of triangle ABC =

Area of triangle DBC =

** (1)**

In and

{Each 90 degrees}

{Vertically Opposite angles}

Therefore, by **AA similarity criterion**, ~

Therefore, ** (2)**

**{Corresponding sides of similar triangles are proportional}**

Putting equation **(2)** in equation **(1), **we get

**Hence Proved**