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# Parallelograms Rectangles Rhombi Squares - PowerPoint PPT Presentation

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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Rhombi Squares

HOMEWORK:

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

5.6/1-13, 28

DEFINITION

Both pairs of opposite sides parallel.

ABCD

A

B

D

C

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

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

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°

Are Supplementary

1

3

2

4

Supplementary angles have a sum of 180

Are Supplementary

145˚

x

x = 180 - 145

x = 35˚

B

C

BX = XD

|

||

X

AX = XC

||

|

A

D

B

C

25

2x-5

A

D

Definition

Rectangles Are Parallelograms With 4 Right Angles

All 4 properties About Parallelograms Are True…

PLUS

• Diagonals are congruent

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

3x-2

3x-2 = 25

25

3x= 27

x = 9

2

3

4

1

11

9

10

12

8

5

7

6

2

3

4

1

11

9

10

12

8

5

7

6

Find the angle measures

37˚

p

b

a

m

k

s

f

r

h

d

t

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

10

3Y + 1 = 10

3Y = 9

Y = 3

3Y + 1

A

B

Remember the Pythagorean thm.

5

AB =

The perimeter Of

rhombus ABCD =

XC =

DB =

3

4

X

20

D

C

3

8

A

B

z

y

y = 50˚

X

z= 30˚

40˚

50˚

D

C

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