Q. 83.6( 8 Votes )

# ABCD is a quadril

Answer : Given, ABCD is a quadrilateral in which AB || DC and AD = BC.

Extend AB to E and draw a line CE parallel to AD.

Since AD||CE and transversal AE cuts them at A and E, respectively. A + E = 180 A = 180 -E

Since, AB||CD and AD||CE

So quadrilateral AECD is a parallelogram.

Now, AD = CE BC = CE

In ΔBCE,

CE = BC

CBE = CEB (opposite angles of equal sides are equal) 180 -B = E 180 -E = B A = B

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 view all courses RELATED QUESTIONS :

The lengthsRS Aggarwal & V Aggarwal - Mathematics

In each of RS Aggarwal & V Aggarwal - Mathematics

If the bisectors RD Sharma - Mathematics

In Fig. 14.113, PRD Sharma - Mathematics

In Fig. 14.114, ARD Sharma - Mathematics

Each side oRS Aggarwal & V Aggarwal - Mathematics

If ABCD is a rhomRD Sharma - Mathematics

If ABCD is a rectRD Sharma - Mathematics