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
caricature
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