Question

e) ABCD is a parallelogram. If its diagonals are equal, find the value of Angle ABC?​

Answer 1

Answer:

answer ABC = 90°

Step-by-step explanation:

Since ABCD is a parallelogram.

Therefore, AB = CD and AD = BC

Thus, in As ABD and ACB,

we have • AD = BC. BD = AC • AB = AB [As approved above] [Given] (common) So,

by SSS criterion of congruence, we have • AABDA ACB GZ BAD = ABC

Now, AD II BC and transversal

AB intersects them at A and B respectively .

... BAD + Z ABC = 180 ° Sum of the interior angles on the same side of a transversal is 180 °)

SZ BAD + 2 ABC = 180 °

B2 Z ABC = 180 °

AZ ABC = 90 °

Hence, the measure of ABC is 90 °