Question

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Show that , if opposite angles of a quadrilateral are
equal , it is a parallelogram.

Answer 1

If the opposite sides in a quadrilateral are equal, then it is a parallelogram. If AB = CD and BC = AD in the given quadrilateral ABCD, then it is a parallelogram. Given: The opposite sides in a quadrilateral ABCD are equal, AB = CD, and BC = AD. To Prove: ABCD is a parallelogram

In the quadrilateral ABCD we are given that AB = CD, and AD = BC. Now compare the two triangles ABC, and CDA. Here we have AC = AC (Common sides), AB = CD (since alternate interior angles are equal), and AD = BC (given). Thus by the SSS criterion both the triangles are congruent, and the corresponding angles are equal. Hence we can conclude that ∠BAC = ∠DCA, and ∠BCA = ∠DAC. Therefore AB // CD, BC // AD, and ABCD is a parallelogram

Answer 2

Answer:

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