Proving Parallelograms

Front

What is a parallelogram?

Back

A parallelogram is a quadrilateral with both pairs of opposite sides parallel.

Front

What are the properties of a parallelogram?

Back

1. Opposite sides are congruent. 2. Opposite angles are congruent. 3. Diagonals bisect each other.

Front

How can you prove that a quadrilateral is a parallelogram using opposite angles?

Back

If both pairs of opposite angles are congruent, then the quadrilateral is a parallelogram.

Front

What is the significance of congruent opposite sides in a parallelogram?

Back

If both pairs of opposite sides are congruent, then the quadrilateral is a parallelogram.

Front

How can you prove that a quadrilateral is a parallelogram using diagonals?

Back

If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram.

Front

What does it mean for two sides to be parallel?

Back

Two sides are parallel if they are always the same distance apart and never meet.

Front

If a quadrilateral has one pair of opposite sides that are both parallel and congruent, what can be concluded?

Back

The quadrilateral is a parallelogram.

Front

What is the midpoint formula?

Back

The midpoint formula is: M = ((x1 + x2)/2, (y1 + y2)/2), used to find the midpoint of a line segment.

Front

How do you find the value of x in a parallelogram?

Back

Set up equations based on the properties of the parallelogram (e.g., opposite sides or angles) and solve for x.

Front

What is the distance formula?

Back

The distance formula is: d = √((x2 - x1)² + (y2 - y1)²), used to find the distance between two points.