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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