ABCD is a parallelogram, if the two diagonals are equal, find the measure of ABC.

Asked by Topperlearning User | 10th Aug, 2017, 12:45: PM

Expert Answer:

AB = CD and AD = BC           (opposite sides of a parallelogram are equal)
In ABD and BAC
AD = BC
BD = AC                               (Given)
AB = BA                                (Common)
ABD BAC                (SSS congurence rule)
BAD = ABC              (c.p.c.t)
AD  BC and transversal AB intersects them at A and B.
BAD +ABC = 180o
ABC +ABC = 180o
 2ABC = 180o
   ABC = 90o
Hence, the measure of ABC = 90o

Answered by  | 10th Aug, 2017, 02:45: PM