Question

which of the following are properties of parallelograms? select all that apply.
parallelograms have opposite parallel sides.
parallelograms have opposite congruent sides.
parallelograms have four right angles.
parallelograms have congruent opposite angles.

Explanation:

1. By definition, a parallelogram is a quadrilateral with two pairs of opposite parallel sides, so "Parallelograms have opposite parallel sides" is a property.
2. In a parallelogram, the opposite sides are congruent (this can be proven using triangle congruence when drawing a diagonal), so "Parallelograms have opposite congruent sides" is a property.
3. A parallelogram does not necessarily have four right angles (that is a property of rectangles, a special type of parallelogram), so this is not a general property of parallelograms.
4. The opposite angles of a parallelogram are congruent (can be proven using the properties of parallel lines and transversals), so "Parallelograms have congruent opposite angles" is a property.

Answer:

• Parallelograms have opposite parallel sides.
• Parallelograms have opposite congruent sides.
• Parallelograms have congruent opposite angles.