Question

Given: ABCD is a parallelogram. Prove: AB CD. What is the reason for proving that AB CD?

A) Corresponding Angles Theorem
B) Parallelogram Side Theorem
C) Vertical Angles Theorem
D) Pythagorean Theorem

Answer 1

To prove that in a parallelogram opposite sides are equal, the Parallelogram Side Theorem is applied, confirming AB is congruent to CD.

Step-by-step explanation:

The problem involves proving that in a parallelogram, opposite sides are equal. When given that ABCD is a parallelogram, we aim to prove that side AB is congruent to side CD. The correct theorem to use here is the Parallelogram Side Theorem, which states that in a parallelogram, opposite sides are congruent (i.e., AB = CD). Therefore, option B) Parallelogram Side Theorem is the right answer choice. This theorem is a property of parallelograms and is distinct from the Pythagorean Theorem, which relates the sides of a right triangle and has no direct application in this proof. The Corresponding Angles Theorem, Vertical Angles Theorem, and the Pythagorean Theorem do not apply directly to the properties of a parallelogram in this context.