Question

Q.2:- Prove that “If pairs of opposite sides of quadrilateral are congruent then that quadrilateral is a parallelogram".​

Answer 1

Answer:

If both pairs of opposite angles of a quadrilateral are congruent, then it's a parallelogram (converse of a property). If the diagonals of a quadrilateral bisect each other, then it's a parallelogram (converse of a property).

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Answer 2

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.