Question

8. Let ABCD be a parallelogram with A on top left, B on top right, D on bottom left and C on the bottom right. Prove that opposite sides of a parallelogram are congruent.

Answer 1

Explanation:

A parallelogram is a quadrilateral with four sides.

Given parallelogram ABCD, to prove that opposite sides of the parallelogram are congruent.

Join D to B, the diagonal of the parallelogram which is also a traversal.

So that;

<ABD = <BDC (alternate angle property)

<BAC = <ACD (alternate angle property)

Also, diagonals;

/AC/ = /BD/ (reflexive property)

Then;

ΔABD = ΔCBD (Angle-Side-Angle, ASA, property)

Thus;

/AB/ ≅ /CD/ (corresponding sides of congruent triangles are congruent)

/BC/ ≅ /AD/ (corresponding sides of congruent triangles are congruent)

Therefore, the opposite sides of the parallelogram ABCD are congruent.