# Show that the diagonals of a parallelogram divide it into four triangles of equal area.

**Solution:**

We know that the diagonals of a parallelogram bisect each other.

Also, the median of a triangle divides it into two triangles of equal areas. By the use of these observations, we can get the required result.

Let's draw a diagram according to the question statement.

We know that diagonals of parallelograms bisect each other. Therefore, O is the mid-point of diagonal AC and BD.

BO is the median in Δ*ABC*. Therefore, BO will divide Δ*ABC* into two triangles of equal areas.

∴ Area (ΔAOB) = Area (ΔBOC) ... (equation 1)

Also, In ΔBCD, CO is the median. Therefore, median CO will divide ΔBCD into two equal triangles.

Hence, Area (ΔBOC) = Area (ΔCOD) ... (equation 2)

Similarly, Area (ΔCOD) = Area (ΔAOD) ... (equation 3)

From Equations equation (1), (2) and (3) we obtain

Area (ΔAOB) = Area (ΔBOC) = Area (ΔCOD) = Area (ΔAOD)

Therefore, we can say that the diagonals of a parallelogram divide it into four triangles of equal area.

**Video Solution:**

## Show that the diagonals of a parallelogram divide it into four triangles of equal area.

### Maths NCERT Solutions Class 9 - Chapter 9 Exercise 9.3 Question 3:

**Summary:**

The diagonals of a parallelogram divide it into four triangles of equal area.