Geometry Notes

Lesson 4.1B

Special Quadrilaterals

Parallelogram

Parallelogram – a quadrilateral with two pairs of opposite sides parallel

Properties of parallelograms

Opposite sides are congruentOpposite angles are congruentDiagonals bisect each other

Rectangle

Rectangle – a parallelogram with four right angles

Special properties of rectangles

Diagonals are congruent

Rhombus

Rhombus – a parallelogram with four congruent sides

Special properties of rhombuses

Diagonals are perpendicularEach diagonal bisects opposite angles

Square Square – a parallelogram with

four right angles and four congruent sides

Special properties of squares

Diagonals are congruent

Diagonals are perpendicular

Each diagonal bisects opposite angles

Kite Kite – A quadrilateral with two

pairs of adjacent sides congruent and no opposite sides congruent

Special properties of kites

.

Diagonals bisect 2 of the angles

Diagonals are perpendicular One diagonal is bisected

Trapezoid Trapezoid – A quadrilateral with

exactly one pair of parallel sides

Special properties of trapezoids

Same-Side Interior Angles = 180

Isosceles Trapezoid

Isosceles Trapezoid – a trapezoid whose nonparallel sides are congruent

Special properties of isosceles trapezoids

.

Nonparallel sides are congruent Base Angles are congruent

Diagonals are congruent

The following is a diagram to show how different quadrilaterals are

related.

True or False?

All parallelograms are squares. False!

Some kites are rectangles. False!

Some parallelograms are rectangles. True!

Some trapezoids are parallelograms. False!

All squares are kites. False!

All squares are rectangles. True!

True or False? All parallelograms are kites. All rectangles are squares. Some kites are squares. All kites are quadrilaterals.

False!

False!

False!

True!

Name ALL special quadrilaterals that satisfy the following conditions.

Both pairs of opposite sides are parallel

Diagonals are perpendicular

All angles are right angles

Parallelogram, rectangle, rhombus, square

rhombus, square, kite

rectangle, square

Name ALL special quadrilaterals that satisfy the following conditions.

Two pairs of opposite sides are equal

All four sides are equal

Both pairs of opposite angles are equal

Parallelogram, rectangle, rhombus, square

rhombus, square

Parallelogram, rectangle, rhombus, square

Name ALL special quadrilaterals that satisfy the following conditions.

Diagonals bisect each other

Both diagonals are equal

Only one pair of sides is parallel

All adjacent pairs of angles are supplementary

Parallelogram, rectangle, rhombus, square

Rectangle, square, Isosceles Trapezoid

Trapezoid, Isosceles Trapezoid

Parallelogram, rectangle, rhombus, square

Fill in the Venn Diagram

Given labels: Parallelograms, Kites, Rectangles

Quadrilaterals

Trapezoids

Squares Rhombuses

EXAMPLES

Draw a quadrilateral with two pairs of opposite parallel sides on the graph.

-5 -1-2-3-4 1 2 3 4

1

2

3

4

5

-1

-2

-3

-4

Examples

Draw a quadrilateral with two pairs of congruent adjacent sides on the graph.

-1-2-3-4 1 2 3 4

1

2

3

4

5

-1

-2

-3

-4

Examples

Use the slope and/or distance formulas to determine the MOST PRECISE name for the quadrilateral with the given vertices.

A (0, 0); B(5, 5); C(8, 4); D(7, 1)

Examples Use the slope and/or distance formulas to determine the MOST

PRECISE name for the quadrilateral with the given vertices.

A(2, 1); B(5, -1); C(4, -4); D(1, -2)