# In Fig.8.1, it is given that BDEF and FDCE are parallelograms. Can you say that BD = CD? Why or why not?

**Solution:**

It is given that

ABC is a __triangle__

D, E and F are the points on BC, CA and AB

BDEF and FDCE are __parallelograms__

We have to prove that BD = CD

In parallelogram BDEF,

BD = EF …. (i) [As the opposite sides of a parallelogram are equal]

In parallelogram FDCE,

CD = EF …. (ii) [As the opposite sides of a parallelogram are equal]

From the equations (i) and (ii)

BD = CD

Therefore, it is proved that BD = CD.

**✦ Try This: **In ∆ABC, AB = 5 cm, BC = 10 cm and CA = 15 cm. If D and E are respectively the mid-points of AB and BC, determine the length of DE.

**☛ Also Check:** NCERT Solutions for Class 9 Maths Chapter 8

**NCERT Exemplar Class 9 Maths Exercise 8.2 Problem 9**

## In Fig.8.1, it is given that BDEF and FDCE are parallelograms. Can you say that BD = CD? Why or why not?

**Summary:**

A quadrilateral will be a parallelogram if its opposite sides are parallel and congruent. In Fig.8.1, it is given that BDEF and FDCE are parallelograms. It is proved that BD = CD

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