Geometry Outline #5 - Parallelograms and Quadrilaterals

Quadrilateral

A polygon with four sides.

Quadrilateral Angle Sum Theorem

The measures of the interior angles of a quadrilateral is 360 degrees.

Rectangle

A quadrilateral with four congruent angles.

Theorem regarding rectangles

Each angle in a rectangle is 90 degrees.

Diagonals in Rectangles

In a rectangle, diagonals are congruent.

Rectangle theorem - diag

If the diagonals of a parallelogram are congruent, then the parallelogram is a rectangle.

Square

A quadrilateral with four congruent sides and four congruent angles.

Theorem regarding squares

All squares are parallelograms.

Relation between square and rhombus

A square is a rhombus and all rhombuses are parallelograms.

Rhombus

A quadrilateral with four congruent sides.

Theorem regarding rhombuses

All rhombuses are parallelograms.

Diagonals in rhombus

In a rhombus, diagonals bisect interior angles.

Parallelogram

A quadrilateral with two pairs of opposite parallel sides.

Biconditional for parallelograms

A quadrilateral is a parallelogram if and only if both pairs of opposite sides are congruent.

Biconditional for angles in parallelograms

A quadrilateral is a parallelogram if and only if both pairs of opposite angles are congruent.

Diagonals bisecting in parallelograms

A quadrilateral is a parallelogram if and only if diagonals bisect each other.

Trapezoid

A quadrilateral with at least one pair of parallel sides.

Kite

A quadrilateral with two distinct pairs of congruent adjacent sides.

Kite Condition

If a kite is a parallelogram, then it is a rhombus.