SECTION 5-6Quadrilaterals and Parallelograms

Mon, Jan 31

ESSENTIAL QUESTIONS

How do you classify different types of quadrilaterals?

What are the properties of parallelograms, and how do you use them?

Where you’ll see this:

Construction, civil engineering, navigation

Mon, Jan 31

VOCABULARY

1. Quadrilateral:

2. Parallelogram:

3. Opposite Angles:

4. Consecutive Angles:

5. Opposite Sides:

6. Consecutive Sides:

Mon, Jan 31

VOCABULARY

1. Quadrilateral: A four-sided figure

2. Parallelogram:

3. Opposite Angles:

4. Consecutive Angles:

5. Opposite Sides:

6. Consecutive Sides:

Mon, Jan 31

VOCABULARY

1. Quadrilateral: A four-sided figure

2. Parallelogram: A quadrilateral with two pairs of parallel sides

3. Opposite Angles:

4. Consecutive Angles:

5. Opposite Sides:

6. Consecutive Sides:

Mon, Jan 31

VOCABULARY

1. Quadrilateral: A four-sided figure

2. Parallelogram: A quadrilateral with two pairs of parallel sides

3. Opposite Angles: In a quadrilateral, the angles that do not

share sides

4. Consecutive Angles:

5. Opposite Sides:

6. Consecutive Sides:

Mon, Jan 31

VOCABULARY

1. Quadrilateral: A four-sided figure

2. Parallelogram: A quadrilateral with two pairs of parallel sides

3. Opposite Angles: In a quadrilateral, the angles that do not

share sides

4. Consecutive Angles: Angles in a quadrilateral that are “next” to

each other; they share a side

5. Opposite Sides:

6. Consecutive Sides:

Mon, Jan 31

VOCABULARY

1. Quadrilateral: A four-sided figure

2. Parallelogram: A quadrilateral with two pairs of parallel sides

3. Opposite Angles: In a quadrilateral, the angles that do not

share sides

4. Consecutive Angles: Angles in a quadrilateral that are “next” to

each other; they share a side

5. Opposite Sides: Sides in a quadrilateral that do not touch each

other

6. Consecutive Sides:

Mon, Jan 31

VOCABULARY

1. Quadrilateral: A four-sided figure

2. Parallelogram: A quadrilateral with two pairs of parallel sides

3. Opposite Angles: In a quadrilateral, the angles that do not

share sides

4. Consecutive Angles: Angles in a quadrilateral that are “next” to

each other; they share a side

5. Opposite Sides: Sides in a quadrilateral that do not touch each

other

6. Consecutive Sides: Sides in a quadrilateral that do touch each

other

Mon, Jan 31

QUADRILATERAL HIERARCHY

Mon, Jan 31

QUADRILATERAL HIERARCHY

Quadrilateral

Mon, Jan 31

QUADRILATERAL HIERARCHY

Quadrilateral4 sides

Mon, Jan 31

QUADRILATERAL HIERARCHY

Quadrilateral4 sides

Trapezoid

Mon, Jan 31

QUADRILATERAL HIERARCHY

Quadrilateral4 sides

Trapezoid1 pair parallel

sides

Mon, Jan 31

QUADRILATERAL HIERARCHY

Quadrilateral4 sides

Trapezoid1 pair parallel

sides

Parallelogram

Mon, Jan 31

QUADRILATERAL HIERARCHY

Quadrilateral4 sides

Trapezoid1 pair parallel

sides

Parallelogram

2 pairs parallelsides

Mon, Jan 31

QUADRILATERAL HIERARCHY

Quadrilateral4 sides

Trapezoid1 pair parallel

sides

Parallelogram

2 pairs parallelsides

Rectangle

Mon, Jan 31

QUADRILATERAL HIERARCHY

Quadrilateral4 sides

Trapezoid1 pair parallel

sides

Parallelogram

2 pairs parallelsides

RectangleOpposite sides

congruent,90° angles

Mon, Jan 31

QUADRILATERAL HIERARCHY

Quadrilateral4 sides

Trapezoid1 pair parallel

sides

Parallelogram

2 pairs parallelsides

RectangleOpposite sides

congruent,90° angles

Rhombus

Mon, Jan 31

QUADRILATERAL HIERARCHY

Quadrilateral4 sides

Trapezoid1 pair parallel

sides

Parallelogram

2 pairs parallelsides

RectangleOpposite sides

congruent,90° angles

Rhombus

4 equalsides

Mon, Jan 31

QUADRILATERAL HIERARCHY

Quadrilateral4 sides

Trapezoid1 pair parallel

sides

Parallelogram

2 pairs parallelsides

RectangleOpposite sides

congruent,90° angles

Rhombus

4 equalsides

Square

Mon, Jan 31

QUADRILATERAL HIERARCHY

Quadrilateral4 sides

Trapezoid1 pair parallel

sides

Parallelogram

2 pairs parallelsides

RectangleOpposite sides

congruent,90° angles

Rhombus

4 equalsides

Square4 equal sides4 90° angles

Mon, Jan 31

PROPERTIES OF PARALLELOGRAMS

Mon, Jan 31

PROPERTIES OF PARALLELOGRAMS

1. Opposites sides are congruent

Mon, Jan 31

PROPERTIES OF PARALLELOGRAMS

1. Opposites sides are congruent

2.Opposite angles are congruent

Mon, Jan 31

PROPERTIES OF PARALLELOGRAMS

1. Opposites sides are congruent

2.Opposite angles are congruent

3.Consecutive angles are supplementary

Mon, Jan 31

PROPERTIES OF PARALLELOGRAMS

1. Opposites sides are congruent

2.Opposite angles are congruent

3.Consecutive angles are supplementary

4.The sum of the angles is 360°

Mon, Jan 31

DIAGONALS OF PARALLELOGRAMS

Mon, Jan 31

DIAGONALS OF PARALLELOGRAMS

5.Diagonals bisect each other

Mon, Jan 31

DIAGONALS OF PARALLELOGRAMS

5.Diagonals bisect each other

6.Diagonals of a rectangle are congruent

Mon, Jan 31

DIAGONALS OF PARALLELOGRAMS

5.Diagonals bisect each other

6.Diagonals of a rectangle are congruent

7.Diagonals of a rhombus are perpendicular

Mon, Jan 31

EXAMPLE 1

a. If AE = 5x - 3 and EC = 15 - x, find AC.

In parallelogram ABCD, diagonals AC and BD intersect at E.

Mon, Jan 31

EXAMPLE 1

a. If AE = 5x - 3 and EC = 15 - x, find AC.

In parallelogram ABCD, diagonals AC and BD intersect at E.

Mon, Jan 31

EXAMPLE 1

a. If AE = 5x - 3 and EC = 15 - x, find AC.

In parallelogram ABCD, diagonals AC and BD intersect at E.

Mon, Jan 31

EXAMPLE 1

a. If AE = 5x - 3 and EC = 15 - x, find AC.

In parallelogram ABCD, diagonals AC and BD intersect at E.

Mon, Jan 31

EXAMPLE 1

a. If AE = 5x - 3 and EC = 15 - x, find AC.

In parallelogram ABCD, diagonals AC and BD intersect at E.

Mon, Jan 31

EXAMPLE 1

a. If AE = 5x - 3 and EC = 15 - x, find AC.

6 6

In parallelogram ABCD, diagonals AC and BD intersect at E.

Mon, Jan 31

EXAMPLE 1

a. If AE = 5x - 3 and EC = 15 - x, find AC.

6 6 x = 3

In parallelogram ABCD, diagonals AC and BD intersect at E.

Mon, Jan 31

EXAMPLE 1

a. If AE = 5x - 3 and EC = 15 - x, find AC.

6 6 x = 3

AE = EC =

In parallelogram ABCD, diagonals AC and BD intersect at E.

Mon, Jan 31

EXAMPLE 1

a. If AE = 5x - 3 and EC = 15 - x, find AC.

6 6 x = 3

AE = EC = 15−3

In parallelogram ABCD, diagonals AC and BD intersect at E.

Mon, Jan 31

EXAMPLE 1

a. If AE = 5x - 3 and EC = 15 - x, find AC.

6 6 x = 3

AE = EC = 15−3 = 12

In parallelogram ABCD, diagonals AC and BD intersect at E.

Mon, Jan 31

EXAMPLE 1

a. If AE = 5x - 3 and EC = 15 - x, find AC.

6 6 x = 3

AE = EC = 15−3 = 12

AC = AE + EC

In parallelogram ABCD, diagonals AC and BD intersect at E.

Mon, Jan 31

EXAMPLE 1

a. If AE = 5x - 3 and EC = 15 - x, find AC.

6 6 x = 3

AE = EC = 15−3 = 12

AC = AE + EC

AC = 12+ 12

In parallelogram ABCD, diagonals AC and BD intersect at E.

Mon, Jan 31

EXAMPLE 1

a. If AE = 5x - 3 and EC = 15 - x, find AC.

6 6 x = 3

AE = EC = 15−3 = 12

AC = AE + EC

AC = 12+ 12

AC = 24

In parallelogram ABCD, diagonals AC and BD intersect at E.

Mon, Jan 31

EXAMPLE 1

a. If AE = 5x - 3 and EC = 15 - x, find AC.

6 6 x = 3

AE = EC = 15−3 = 12

AC = AE + EC

AC = 12+ 12

AC = 24 units

In parallelogram ABCD, diagonals AC and BD intersect at E.

Mon, Jan 31

EXAMPLE 1

b. If DE = 4y + 1 and EB = 5y - 1, find DB.

In parallelogram ABCD, diagonals AC and BD intersect at E.

Mon, Jan 31

EXAMPLE 1

b. If DE = 4y + 1 and EB = 5y - 1, find DB.

4y + 1 = 5y − 1

In parallelogram ABCD, diagonals AC and BD intersect at E.

Mon, Jan 31

EXAMPLE 1

b. If DE = 4y + 1 and EB = 5y - 1, find DB.

4y + 1 = 5y − 1 −4y −4y +1 +1

In parallelogram ABCD, diagonals AC and BD intersect at E.

Mon, Jan 31

EXAMPLE 1

b. If DE = 4y + 1 and EB = 5y - 1, find DB.

4y + 1 = 5y − 1 −4y −4y +1 +1

2 = y

In parallelogram ABCD, diagonals AC and BD intersect at E.

Mon, Jan 31

EXAMPLE 1

b. If DE = 4y + 1 and EB = 5y - 1, find DB.

DE = EB = 4y + 1 = 5y − 1 −4y −4y +1 +1

2 = y

In parallelogram ABCD, diagonals AC and BD intersect at E.

Mon, Jan 31

EXAMPLE 1

b. If DE = 4y + 1 and EB = 5y - 1, find DB.

DE = EB = 4(2)+ 1 4y + 1 = 5y − 1 −4y −4y +1 +1

2 = y

In parallelogram ABCD, diagonals AC and BD intersect at E.

Mon, Jan 31

EXAMPLE 1

b. If DE = 4y + 1 and EB = 5y - 1, find DB.

DE = EB = 4(2)+ 1 = 9 4y + 1 = 5y − 1 −4y −4y +1 +1

2 = y

In parallelogram ABCD, diagonals AC and BD intersect at E.

Mon, Jan 31

EXAMPLE 1

b. If DE = 4y + 1 and EB = 5y - 1, find DB.

DE = EB = 4(2)+ 1 = 9

DB = DE + EB 4y + 1 = 5y − 1

−4y −4y +1 +1

2 = y

In parallelogram ABCD, diagonals AC and BD intersect at E.

Mon, Jan 31

EXAMPLE 1

b. If DE = 4y + 1 and EB = 5y - 1, find DB.

DE = EB = 4(2)+ 1 = 9

DB = DE + EB

DB = 9+9

4y + 1 = 5y − 1 −4y −4y +1 +1

2 = y

In parallelogram ABCD, diagonals AC and BD intersect at E.

Mon, Jan 31

EXAMPLE 1

b. If DE = 4y + 1 and EB = 5y - 1, find DB.

DE = EB = 4(2)+ 1 = 9

DB = DE + EB

DB = 9+9

DB = 18

4y + 1 = 5y − 1 −4y −4y +1 +1

2 = y

In parallelogram ABCD, diagonals AC and BD intersect at E.

Mon, Jan 31

EXAMPLE 1

b. If DE = 4y + 1 and EB = 5y - 1, find DB.

DE = EB = 4(2)+ 1 = 9

DB = DE + EB

DB = 9+9

DB = 18 units

4y + 1 = 5y − 1 −4y −4y +1 +1

2 = y

In parallelogram ABCD, diagonals AC and BD intersect at E.

Mon, Jan 31

EXAMPLE 2

a. In quadrilateral ABCD, diagonals AC and BD intersect at E.

What special quadrilateral must ABCD be so that △AED is an

isosceles triangle? Draw a picture first.

Mon, Jan 31

EXAMPLE 2

Discuss on edmodo, have an answer for class tomorrow

a. In quadrilateral ABCD, diagonals AC and BD intersect at E.

What special quadrilateral must ABCD be so that △AED is an

isosceles triangle? Draw a picture first.

Mon, Jan 31

EXAMPLE 2

b. In rectangle ABCD, diagonals AC and BD intersect at E.

Which pair of triangles is not congruent? Draw a picture first.

Mon, Jan 31

EXAMPLE 2

b. In rectangle ABCD, diagonals AC and BD intersect at E.

Which pair of triangles is not congruent? Draw a picture first.

Discuss on edmodo, have an answer for class tomorrow

Mon, Jan 31

EXAMPLE 2

a. XZ b. m∠YXZ

c. m∠XYW d. ZW

c. A woodworker makes parallel cuts XY and ZW in a board.

The edges of the board, XZ and YW are also parallel.

YW = 21.5 in. Find each measure, if possible.

Mon, Jan 31

EXAMPLE 2

a. XZ b. m∠YXZ

c. m∠XYW d. ZW

21.5 in.

c. A woodworker makes parallel cuts XY and ZW in a board.

The edges of the board, XZ and YW are also parallel.

YW = 21.5 in. Find each measure, if possible.

Mon, Jan 31

EXAMPLE 2

a. XZ b. m∠YXZ

c. m∠XYW d. ZW

21.5 in. 135°

c. A woodworker makes parallel cuts XY and ZW in a board.

The edges of the board, XZ and YW are also parallel.

YW = 21.5 in. Find each measure, if possible.

Mon, Jan 31

EXAMPLE 2

a. XZ b. m∠YXZ

c. m∠XYW d. ZW

21.5 in. 135°

45°

c. A woodworker makes parallel cuts XY and ZW in a board.

The edges of the board, XZ and YW are also parallel.

YW = 21.5 in. Find each measure, if possible.

Mon, Jan 31

EXAMPLE 2

a. XZ b. m∠YXZ

c. m∠XYW d. ZW

21.5 in. 135°

45° Not enough info

c. A woodworker makes parallel cuts XY and ZW in a board.

The edges of the board, XZ and YW are also parallel.

YW = 21.5 in. Find each measure, if possible.

Mon, Jan 31

PROBLEM SET

Mon, Jan 31

PROBLEM SET

p. 218 #1-43 odd

“Make visible what, without you, might perhaps never have

been seen.” - Robert Bresson

Mon, Jan 31