# D and E are points on sides AB and AC respectively of ∆ ABC such that ar (DBC) = ar (EBC). Prove that DE || BC.

**Solution:**

If two triangles are on a common base and have equal areas, then they will lie between the same parallel lines.

Let's draw the given triangle ABC.

Given that ar (DBC) = ar (EBC)

Since ΔEBC and ΔDBC are lying on a common base BC and they also have equal areas, therefore, ΔEBC and ΔDBC will lie between the same parallel lines.

Hence, DE || BC proved.

**Video Solution:**

## D and E are points on sides AB and AC respectively of ∆ ABC such that ar (DBC) = ar (EBC). Prove that DE || BC.

### Maths NCERT Solutions Class 9 - Chapter 9 Exercise 9.3 Question 7:

**Summary:**

If D and E are points on sides AB and AC respectively of such that ar (DBC) = ar (EBC), then DE||BC.