Explore Properties and Proofs of Parallelograms

Front

What is a parallelogram?

Back

A parallelogram is a four-sided figure (quadrilateral) with opposite sides that are parallel and equal in length.

Front

What are the properties of a parallelogram?

Back

1. Opposite sides are equal in length. 2. Opposite angles are equal. 3. The diagonals bisect each other. 4. Consecutive angles are supplementary.

Front

How do you prove that a quadrilateral is a parallelogram?

Back

To prove a quadrilateral is a parallelogram, show that either: 1. Both pairs of opposite sides are equal. 2. Both pairs of opposite angles are equal. 3. The diagonals bisect each other.

Front

What is the relationship between the diagonals of a parallelogram?

Back

The diagonals of a parallelogram bisect each other, meaning they cut each other in half.

Front

If one angle of a parallelogram is 70 degrees, what are the measures of the other angles?

Back

The opposite angle is also 70 degrees, and the consecutive angles are supplementary, so each measures 110 degrees.

Front

What is the formula for the area of a parallelogram?

Back

Area = base × height.

Front

How do you find the height of a parallelogram?

Back

The height can be found by drawing a perpendicular line from the base to the opposite side.

Front

What is a rectangle in relation to parallelograms?

Back

A rectangle is a type of parallelogram where all angles are right angles (90 degrees).

Front

What is a rhombus in relation to parallelograms?

Back

A rhombus is a type of parallelogram where all sides are of equal length.

Front

What is the difference between a square and a parallelogram?

Back

A square is a special type of parallelogram where all sides are equal and all angles are right angles.