Question

ABCD is a parallelogram. If its diagonals are equal, then what is the value of ∠ABC.

Answer 1

Step-by-step explanation:

Since ABCD is a parallelogram. Therefore,

AB=CD and AD=BC

Thus, in △s ABD and ACB,

AD=BC

BD=AC

AB=AB

So, by SSS criterion of congruence,

△ABD≅△ACB

Therefore, ∠BAD=∠ABC

Now, AD∥BC and transversal AB intersects them at A and B respectively.

Therefore,

∠BAD+∠ABC=180

o

∠ABC+∠ABC=180

o

2∠ABC=180

o

∠ABC=90

o

Hence, the measure of ∠ABC is 90

o

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