3.2 Properties of Quadrilaterals

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Warm up

1. Factor & Solve: a. x

2

+ 9x + 14 = 0 x = -7, -2 b. x

2

+ 2x -15 = 0 c.

x = -5, 3 x

2

– 7x + 15 =45 x = 10, -3

2.

√4 = _____

(this has 2 answers)

3.

√9 = _____

(this has 2 answers)

4.

5. Use substitution to solve: y = 3x + 4 and 3x + 2y = 17

X = 1, y = 7

3.2 Properties of

Quadrilaterals

♥Any four sided polygon is a quadrilateral.

♥We’ll study special quadrilaterals in this section:

♥Trapezoid

♥Trapezium

♥Parallelogram

♥Rhombus

♥Rectangle

♥Square

♥Kite

Properties of a TRAPEZIUM:

A quadrilateral with NO parallel sides.

A special Trapezium is a

KITE

♥ 2 pair of consecutive congruent sides

♥ Opposite sides are NOT congruent

♥ Diagonals are perpendicular

♥ Notice only ONE diagonal is bisected

Properties of a trapezoid

♥ A trapezoid has one and only one pair of parallel sides.

Properties of parallelograms

♥ Opposite sides of a parallelogram are parallel

♥ Opposite sides are congruent

♥ Opposite angles of a parallelograms are congruent.

♥ Diagonals of a parallelogram bisect each other

♥ Consecutive angles of a parallelogram are supplementary supplementary

Properties of a Rhombus (Rhombi)

♥ A rhombus is a parallelogram (this means it has

ALL of the characteristics of a parallelogram)

In addition:

♥ A rhombus has four congruent sides

♥ The diagonals of a rhombus are perpendicular

♥ The diagonals bisect opposite angles

Properties of Rectangles

♥ A rectangle is a parallelogram (this means it has ALL the characteristics of a parallelogram)

IN ADDITION:

♥ Four right angles

♥ The diagonals of a rectangle are congruent and they bisect each other

Properties of Squares

♥ A square is a parallelogram, a rectangle, and a rhombus (It has ALL those characteristics!!!)

♥ Has four congruent sides

♥ Has four right angles

♥ The diagonals of a square

:

♥ bisect each other

♥ are congruent

♥ are perpendicular

.

♥ Bisect opposite angles

Cut and sort

• Go to the back of the room and get worksheets 2-15A and 2-15B and a pair of scissors

• Your instructions are on 2-15B

• Have fun Ü

• Then complete 2-16

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