Q. 24

ABCD is a p

Answer :

To Prove: DF = 2DL

Given: ABCD is a parallelogram. E is the midpoint of AD. DL || EB meeting AB produced at F and BC at L.


Concept Used:


Converse Midpoint Theorem: A line drawn through the mid-point of any side of a triangle and parallel to another side, bisects the third side.


Opposite sides of a parallelogram are parallel and equal to each other.


Diagram:



Proof:


In ΔADF,


E is the midpoint of AD and EB || DF


B is the mid-point of AF [Converse mid-point theorem]


In ΔADF,


E and B are the midpoints AD and AF respectively


By mid-point theorem, we have,


EB = 1/2 DF.........(1)


Since EB || DL and BL || ED.


Opposite sides are parallel, and therefore, EBLD is a parallelogram.


EB = DL......(2) [opposite sides of a parallelogram are equal]


DL = 1/2 DF [L is the midpoint of DF]


LF = DL = EB


Therefore, EB = LF


Now, 1/2 DF = DL.


Hence, DF = 2 DL


Hence, Proved.


Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
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
caricature
view all courses
RELATED QUESTIONS :

The figure formedRS Aggarwal & V Aggarwal - Mathematics

A <imRS Aggarwal & V Aggarwal - Mathematics

In a parallelpgraRD Sharma - Mathematics