Quadrilateral Analysis: Testing Parallelogram Properties with Sides 20 and 8

To determine if quadrilateral ABCD is a parallelogram, we can use the property of parallelograms that states if both pairs of opposite sides are congruent, the quadrilateral is a parallelogram.

Given:

• $AB = 20$
• $CD = 20$
• $BD = 8$
• $AC = 8$

Step 1: Identify opposite sides $AB$ and $CD$.

Both sides $AB$ and $CD$ are given to be 20. Thus, they are congruent.

Since both pairs of opposite sides $AB$ and $CD$ are equal (and it is implied that $AD = BC$ by construction shown), we utilize the theorem for parallelograms:

• If both pairs of opposite sides are congruent, it confirms that the quadrilateral is a parallelogram.

Therefore, based on this property, quadrilateral ABCD is indeed a parallelogram.

The final answer is Yes.