Quadrilaterals

Quadrilateral

A four-sided polygon

Parallelogram

A quadrilateral in which both pairs of opposite sides are parallel.

Rectangle

A parallelogram in which at least one angle is a right angle.

Rhombus

A parallelogram in which at least two consecutive sides are congruent.

Kite

A quadrilateral in which two dis-joint pairs of consecutive sides are congruent.

Square

A parallelogram that is both a rectangle and a rhombus.

Trapezoid

A quadrilateral with exactly one pair of parallel sides. The parallel sides are called bases of the trapezoid.

Isosceles trapezoid

A trapezoid in which the nonparallel sides (legs) are congruent.

Properties of Parallelogram

1. The opposite sides are parallel

2. The opposite sides are congruent

3. The opposite angles are congruent

4. The diagonals bisect each other

5. Any pair of consecutive angles are supplementary

Properties of Rectangles

1. All the properties of a parallelogram apply by definition

2. All angles are right angles

3. The diagonals are congruent

Properties of Kites

1. Two disjoint pairs of consecutive sides are congruent by definition

2. The diagonals are perpendicular

3. One diagonal is the perpendicular bisector of the other

4. One of the diagonals bisects a pair of opposite angles

5. One pair of opposite angles are congruent

Properties of Rhombuses

1. All of the properties of a parallelogram apply by definition

2. All of the properties of a kite apply (in fact, the half properties become full properties)

3. All sides are congruent (i.e. it is equilateral)

4. Diagonals bisect all of the angles

5. Diagonals are perpendicular bisectors of each other

6. Diagonals divide the rhombus into four congruent right triangles.

Properties of Squares

1. All the properties of a rectangle apply by definition

2. All the properties of a rhombus apply by definition

3. The diagonals form four isosceles right triangles

Properties of Isosceles Trapezoids

1. The legs are congruent by definition

2. The bases are parallel (by definition of trapezoid)

3. The lower base angles are congruent

4. The upper base angles are congruent

5. The diagonals are congruent

6. Any lower base angle is supplementary to any upper base angle

Properties of Trapezoids

1. 2 sets of consecutive angles are supplementary

2. Exactly pair of opposite sides are parallel