Question

Parallelogram ABCD contains two congruent triangles. Use these triangles to prove, in two or more complete sentences, the congruence of opposite sides in parallelogram ABCD based on the principles of SSS (side-side-side), SAS (side-angle-side), and AAS (angle-angle-side).

Answer 1

Opposite sides of parallelogram ABCD can be proved congruent using the principle of SSS by comparing the congruent triangles within the parallelogram.

Step-by-step explanation:

To prove the congruence of opposite sides in parallelogram ABCD using the principles of SSS, SAS, and AAS, we can start by considering the congruent triangles within the parallelogram.

Let's call them Triangle A and Triangle B.

Triangle A can be proved congruent to Triangle B using the SSS principle, since they have three pairs of congruent sides.

As a parallelogram, opposite sides of ABCD are congruent, so we can conclude that the opposite sides of the parallelogram are congruent based on the congruence of Triangle A and Triangle B.