Question

ABCD is a parallelogram. If the two diagonals are equal, find the measure of ∠ABC.​

Answer 1

ANSWER

Since ABCD is a parallelogram. Therefore,

AD=BC

AB= CD

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

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2∠ABC= 180

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∠ABC= 90

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Hence, the measure of ∠ABC is 90

o

Answer:

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