1.6 Classifying Quadrilaterals

Homework:

Lesson 1.6/1-13, 15-18

Quiz Friday on Lessons 1.5 – 1.7

1.6 Classifying Quadrilaterals

What is a Quadrilateral?

A polygons with exactly four sides

Special Quadrilaterals

Quadrilaterals with specific characteristics. Parallelogram Rectangle Rhombus Square Trapezoid Kite

Parallelogram

Parallelogram: A Quadrilateral with both pairs of opposite sides parallel

Rhombus

Rhombus: A parallelogram with four congruent sides

Rectangle Rectangle: A parallelogram with four

right angles

Square Square: A parallelogram with four congruent sides

and four right angles (it is a rhombus and a rectangle) A Square is a Regular Parallelogram

Kite Kite: A quadrilateral with two pairs of

consecutive congruent sides no opposite sides congruent no parallel sides

Trapezoid Trapezoid: A quadrilateral with exactly

one pair of parallel sides

Isosceles Trapezoid: Trapezoid with legs (nonparallel sides) congruent

Quadrilateral Family Tree

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

A rhombus is a parallelogram with four congruent sides.

A rectangle is a parallelogram with four right angles.

A square is a parallelogram with four congruent sides and right angles.

A kite is a quadrilateral with two pairs of adjacent sides congruent and no opposite sides congruent.A trapezoid is a quadrilateral with exactly one pair of parallel sides. The isosceles trapezoid at the right is a trapezoid whose nonparallel sides (legs) are congruent.

Classifying Quadrilaterals

Judging by appearance, classify each quadrilateral in as many ways as possible:

SquareRectangleRhombus

ParallelogramQuadrilateral

ParallelogramQuadrilateral

Classifying Quadrilaterals

Judging by appearance, classify each quadrilateral in as many ways as possible:

RhombusParallelogramQuadrilateral

TrapezoidQuadrilateral

Classifying Quadrilaterals

Judging by appearance, classify each quadrilateral in as many ways as possible:

RectangleParallelogramQuadrilateral

KiteQuadrilateral

Using Properties

Find the value of the variables for the kite:

x + 6

3x - 52x + 4

2y + 5

T

K

B

J

JB = KB2x + 4 = 3x – 5

-x = -9x = 9

TK = 9 + 6TK = 15

TJ => 2y + 5 = 15 2y = 10 y = 5

Using Properties

Find the values of the variables for the rhombus:

3b + 2

3a + 8

4b - 2

5a + 4

3b + 2 = 4b -2b = 4

5a + 4 = 3a + 82a = 4a = 2

Complete each statement.

1. A quadrilateral with four right angles is a

_________.

2. A parallelogram with four right angles and four

congruent sides is a _______.

3. A figure with 4 sides and 4 angles is a ______.

4. Give the most descriptive name for this

quadrilateral.

Lesson Quiz

square

square or rectangle

quadrilateral

trapezoid

1

2

3

4