# D, E and F are re

(i) In triangle ABC it is given that,

EF is parallel to BC

And,

The Midpoint Theorem states that the segment joining two sides of a triangle at the midpoints of
those sides is parallel to the third side and is half the length of the third side.

EF = BC   ( By using Mid – point theorem)

Also,

BD = BC (As D is the mid-point)

So,

BD = EF

BF and DE also parallel to each other

Therefore, the pair of opposite sides are equal and parallel in length.
Similarly BF = DE

Therefore,

BDEF is a parallelogram

(ii) Diagonal of a parallelogram divides it into two equal area

Therefore,

In parallelogram BDEF
DF is the diagonal

⇒ Area of triangle BFD = Area of triangle DEF  ......(1)
In parallelogram DCEF

ED is the diagonal

⇒  Area of triangle AFE = Area of triangle DEF   .....(2)

In parallelogram AFDE
EF is the diagonal.

⇒ Area of triangle CDE = Area of triangle DEF  ......(3)

So from (1), (2) and (3)

Area of triangle BFD = Area of triangle AFE = Area of triangle CDE = Area of triangle DEF

Area of triangle ABC = Area of triangle BFD + Area of triangle AFE + Area of triangle CDE + Area of triangle DEF

4 (Area of triangle DEF) = Area of triangle ABC

Area of triangle DEF = × Area of triangle

(iii) Area of parallelogram BDEF = Area of triangle DEF + Area of triangle BDE

From part (ii)

Area of parallelogram BDEF = Area of triangle DEF + Area of triangle DEF

= 2 × Area of triangle DEF

= 2 ×  × Area of triangle ABC

= × Area of triangle ABC

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Revision on Angle sum Property of Triangles44 mins
Surface Area and Volume of solids Revision43 mins
Arc of Circle And Related IMP Qs40 mins
Circles- All kinds of Questions36 mins
Sphere and Hemisphere42 mins
Trigonometric Identities - Marathon Part 146 mins
Test what you Know Quiz44 mins
Heron's Formula- Full Gyan46 mins
Introduction to Lines and Angles60 mins
Master the Art of Writing Chemical Formulae42 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
view all courses