Warm Up May 8th

1. Find the slope between (5, 8) and (3, -6).

2. Find the distance, and midpoint between A and B where A(12, 4) B(5, 9).

3. Write the equation of a line that is perpendicular to the given equation 4x - 3y = 8, and goes through the point (3, 2).

QUIZ #6

• You may use your notes but NOT your classmates!

Properties of

Quadrilaterals

Quadrilateral

• Four sided polygon• Closed, straight sides• Examples: square, rectangle, diamond,

etc.

Parallelogram

• A quadrilateral with both pairs of opposite sides parallel.

• We use the symbol

Diagonals of a Parallelogram• If a quadrilateral is a parallelogram, then its

diagonals BISECT each other.

AC bisects DB

AE = EC and DE = EB

• The altitude (or height) of a parallelogram is the perpendicular distance from the base to the opposite side (which may have to be extended).

• In the figure above, the altitude, h, corresponding to the base AD is shown.

• Parallelograms are the "parent" of some other quadrilaterals, which are obtained by adding restrictions:

• A rectangle is a parallelogram but with all four interior angles fixed at 90°

• A rhombus is a parallelogram but with all sides equal in length

• A square is a parallelogram but with all sides equal in length and all angles fixed at 90°

Rectangle • All right angles (90°).

• Opposite sides are parallel and congruent.

• The diagonals bisect each other.

• The diagonals are congruent.

Rhombus • All four sides are the same length.

• Also its diagonals are perpendicular.

• Opposite sides are parallel.

Square• All right angles (90°).

• All four sides are the same length.

• Also its diagonals are perpendicular.

• Opposite sides are parallel.

• Diagonals are congruent.

Trapezoid • A quadrilateral with exactly one pair of

parallel sides

Isosceles Trapezoid

• A trapezoid with congruent legs

• A quadrilateral with exactly one pair of parallel sides

Homework

• Worksheet

Area and Perimeter of Quadrilaterals

May 9th, 2013

Warm Up May 9th 1. Which quadrilateral has diagonals that are

perpendicular?

2. Which quadrilateral has diagonals that are perpendicular, and all angles are (90°)?

3. Which quadrilateral has only one set of parallel sides?

4. What is the slope of the second diagonal of a rhombus, if the first diagonal has a slope of 5?

Rhombus, Rectangle, Square

• Rhombus-parallelogram with four congruent sides

• Rectangle- parallelogram with four right angles

• Square-parallelogram with four congruent sides and four right angles

Sometimes, Always, Never

• A rhombus is a rectangle• A rhombus is a square

• A square is a rhombus• A square is a rectangle

• A rectangle is a rhombus• A rectangle is a square

SometimesSometimes

AlwaysALWAYS

SometimesSometimes

Perimeter of a Parallelogram.

Perimeter = 2(w + h)

w = base length of the parallelogram

h = side length

5 ft

Area of a Parallelogram

• This can be found by multiplying a base by the corresponding altitude.

A = bh

Perimeter of a Rectangle

Perimeter = 2(w+h)

w = width of the rectangleh = height of the rectangle

30

15

Area of a Rectangle

Area = lw

w  = width

l  = length

30

15

Perimeter of a Rhombus

Perimeter = 4s

S = length of any one side

Area of a Rhombus

Area = ba

b is the length of the basea is the altitude (height)

Perimeter of a Square

Perimeter = 4s

s = length of one side

Area of a Square

Area = s2

s = length of one side

Perimeter of a Trapezoid

Perimeter = a + b + c + d

a, b, c, d = lengths of each side

9 cm

Area of a Trapezoid

b1, b2 = lengths of each

baseh = altitude (height)

hbbA 212

1

Triangle and Rhombus Flap• Four sided figure.• All sides same length. • Diagonals are

perpendicular.• Opposite sides

parallel.

P = 4s

A = ba (altitude)

Three sided figure.

sides all add2

1

P

bhA

Parallelogram & Rectangle Flap

• Both pairs of opposite sides parallel.

• Diagonals BISECT each other.

P = 2(w + h)

A = bh

•All right angles (90°).

•Opposite sides are parallel and congruent.

•Diagonals bisect each other.

•Diagonals are congruent.

•P = 2(w+h) •A = lw

Trapezoid Flap

• Exactly one pair of parallel sides

• Isosceles trapezoids have congruent legs

P = add all sides

hbbA 212

1

Homework

• Worksheet