# ABCD is a trapezi

Let EF intersect DB at G

By converse of mid-point theorem, we know that a line drawn through the mid-point of any side of a triangle and parallel to another side, bisects the third side

In ΔABD,

EF || AB and E is the mid-point of AD

Therefore,

G will be the mid-point of DB

EF || AB and

AB || CD

EF || CD (Two lines parallel to the same line are parallel to each other)

In ΔBCD,

GF || CD and

G is the mid-point of line BD. Therefore, by using converse of mid-point theorem, F is the mid-point of BC

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
view all courses
RELATED QUESTIONS :

E and F are respeNCERT Mathematics Exemplar

In a triangle, P,RD Sharma - Mathematics

In Fig. 14.99, ABRD Sharma - Mathematics

In Fig. 14.100, ARD Sharma - Mathematics

Prove that RS Aggarwal & V Aggarwal - Mathematics

Show that tRS Aggarwal & V Aggarwal - Mathematics

In the adjoRS Aggarwal & V Aggarwal - Mathematics

In the adjoRS Aggarwal & V Aggarwal - Mathematics

The parallel sideRS Aggarwal & V Aggarwal - Mathematics

In the given figuRS Aggarwal & V Aggarwal - Mathematics