1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

# D, E and F are respectively the mid-points of the sides BC, CA and AB of a ABC. Show that

A
BDEF is a parallelogram
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B
Area of DEF = 1/4 area of ABC
No worries! Weâ€˜ve got your back. Try BYJUâ€˜S free classes today!
C
Area of BDEF = 1/2 of area of ABC
No worries! Weâ€˜ve got your back. Try BYJUâ€˜S free classes today!
D
None of these
No worries! Weâ€˜ve got your back. Try BYJUâ€˜S free classes today!
Open in App
Solution

## The correct option is A BDEF is a parallelogramGiven :△ABC where D, E, F are mid-points of BC, AC and AB respectively.To prove : BDEF is a parallelogram.Proof :In △ABC,F is mid-point of AB,E is mid-point of ACLine segments joining the mid-points of two sides of a triangle is parallel to the third side.Therefore, FE∥BCFE∥BD ( Parts of parallel lines are parallel )D is the mid-point of BC and E is the mid-point of AC.Therefore, DE∥ABDE∥FBNow, FE∥BD and DE∥FBIn BDEF, both pairs of opposite sides are parallel.Therefore, BDEF is a parallelogram.

Suggest Corrections
0
Join BYJU'S Learning Program
Related Videos
Section Formula
MATHEMATICS
Watch in App
Explore more
Join BYJU'S Learning Program