# In Fig. 9.31, ABCD, DCFE and ABFE are parallelograms. Show that ar (ADE) = ar (BCF).

**Solution:**

We can see that the sides of triangles ADE and BCF are also the opposite sides of the given parallelograms. Now, we can show both the triangles congruent by SSS congruency.

Also, we know that congruent triangles have equal areas.

It is given that ABCD is a parallelogram. We know that opposite sides of a parallelogram are equal.

∴ AD = BC ... (1)

Similarly, for parallelograms DCFE and ABFE, it can be said that DE = CF ... (2)

and, EA = FB ... (3)

In ΔADE and ΔBCF,

AD = BC [Using equation (1)]

DE = CF [Using equation (2)]

EA = FB [Using equation (3)]

∴ ΔADE ≅ ΔBCF (SSS congruence rule)

The SSS rule states that if three sides of one triangle are equal to three sides of another triangle, then the triangles are congruent.

∴ Area (ΔADE) = Area (ΔBCF)

**Video Solution:**

## In Fig. 9.31, ABCD, DCFE and ABFE are parallelograms. Show that ar (ADE) = ar (BCF).

### Maths NCERT Solutions Class 9 - Chapter 9 Exercise 9.4 Question 3:

**Summary:**

If ABCD, DCFE, and ABFE are parallelograms in the given figure, ar (ΔADE) = ar (ΔBCF) since ΔADE ≅ ΔBCF by SSS congruence.