Question

Prove that if opposite sides of any quadrilateral are equal then the quadrilateral will be a parallelogram​

Answer 1

Answer:

Given: Quadrilateral ABCD in which AB = DC and AD = BC$$

To prove: ABCD is a parallelogram.

Construction: Draw diagonal AC.

Proof: Some statements and reasons for their validity are given below:

Statement Reason

AD=BC Given

AB=CD Given

AC=AC Common

△CBA≅△ADC By SSS postulate

∠DCA=∠BAC Corresponding angles of congruent triangles

DC∥AB Alternate angles are equal.

∠DAC=∠BCA Corresponding angles of congruent triangles

AD∥BC Alternate angles are equal.

It follows that ABCD is a parallelogram.

Step-by-step explanation:

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Answer 2

Answer:

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