# Parallelograms Rectangles Rhombi Squares - PowerPoint PPT Presentation

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Parallelograms Rectangles Rhombi Squares. HOMEWORK: 5.5/1-6, 9-11,16, 17 5.6/1-13, 28. Parallelograms. DEFINITION. Parallelograms are quadrilaterals with Both pairs of opposite sides parallel. ABCD. ›. A. B. ›. ›. ›. ›. ›. D. C. 4 Properties of Parallelograms. Definition

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Parallelograms Rectangles Rhombi Squares

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Parallelograms Rectangles

Rhombi Squares

HOMEWORK:

5.5/1-6, 9-11,16, 17

5.6/1-13, 28

Parallelograms

DEFINITION

Both pairs of opposite sides parallel.

ABCD

A

B

D

C

4 Properties of Parallelograms

Definition

Quadrilateral with both pairs opposite sides parallel

Properties

1) Both Pairs Opp Sides Congruent

2) Both Pairs Opp Angles Congruent

3) Consecutive Angles Supplementary

4) Diagonals Bisect Each Other

Both Pairs Opp Sides Parallel

A

B

AB||DC

1 and 6

3 and 8

2 and 5

4 and 7

1

3

2

4

7

5

8

6

D

C

Alternate Int Angles Are Congruent

Both Pairs Opp Sides Congruent

X = 23

2Y – 16 = 42

2Y = 58

Y = 29

23

42

2Y - 16

X

### Both Pairs Opposite Angles Congruent

X = 65

5Y – 5 = 115

5Y = 120

Y = 24

5Y - 5

X

115°

65°

Consecutive Angles

Are Supplementary

1

3

2

4

Supplementary angles have a sum of 180

Consecutive Angles

Are Supplementary

145˚

x

x = 180 - 145

x = 35˚

Diagonals Bisect Each Other

B

C

BX = XD

|

||

X

AX = XC

||

|

A

D

Diagonals Bisect Each Other

B

C

25

2x-5

A

D

RECTANGLES

Definition

Rectangles Are Parallelograms With 4 Right Angles

All 4 properties About Parallelograms Are True…

PLUS

• Diagonals are congruent

All Angles = 90°

If 1 Angle In A Parallelogram Is A Right

Angle, Then All 4 Angles Are Right Angles

This gives us

right triangles also

|

|

|

|

Diagonals Are Congruent

This Gives Us 4 Congruent Segments

And 4 Isosceles Triangles

This Tells Us A Lot About The Angles

Diagonals Are Congruent

3x-2

3x-2 = 25

25

3x= 27

x = 9

Congruent Pairs of Angles

2

3

4

1

11

9

10

12

8

5

7

6

Congruent Pairs of Angles

2

3

4

1

11

9

10

12

8

5

7

6

Congruent Pairs of Angles

Find the angle measures

37˚

p

b

a

m

k

s

f

r

h

d

t

RHOMBI

Definition

A Rhombus Is A Parallelogram With

4 Congruent Sides

All 4 properties About Parallelograms Are True…

PLUS

• Diagonals are perpendicular

• Diagonals bisect opposite angles

4 congruent sides

10

3Y + 1 = 10

3Y = 9

Y = 3

3Y + 1

Diagonal are perpendicular

A

B

Remember the Pythagorean thm.

5

AB =

The perimeter Of

rhombus ABCD =

XC =

DB =

3

4

X

20

D

C

3

8

Diagonals bisect opposite angles

A

B

z

y

y = 50˚

X

z= 30˚

40˚

50˚

D

C

SQUARE

The Square Is The Most Special Of All !!

Everything That’s True For

All The Others Is True For Squares.

SQUARE

Regular Parallelogram

Definitions

Equiangular Rhombus

Equilateral Rectangle

Equiangular

Equilateral

Diagonals ≅ & ┴

diagonals bisect each other

diagonals bisect opposite <‘s

Opposite <‘s ≅

Opposite sides ≅

Consecutive <‘s = 180˚

Has all the properties of the parallelogram, rectangle and rhombus

PARALLELOGRAMS

RECTANGLES

RHOMBI

SQUARES

4 sides, angles add to 360

Parallelograms

Opp sides parallel, Opp sides congruent, Opp angles congruent,

Consecutive angles =180, Diagonals bisect

Rhombus

All sides are congruent.

Diagonals are perpendicular.

Opp angles are bisected.

Rectangle

All angles are congruent.

Diagonals are congruent.

Square

Everything