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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

Parallelograms Rectangles

Rhombi Squares

HOMEWORK:

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

5.6/1-13, 28


Parallelograms rectangles rhombi squares

Parallelograms

DEFINITION

Parallelograms are quadrilaterals with

Both pairs of opposite sides parallel.

ABCD

A

B

D

C


Parallelograms rectangles rhombi squares

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


Parallelograms rectangles rhombi squares

Both Pairs Opp Sides Parallel

Add a transversal and ..

A

B

AB||DC

1 and 6

3 and 8

AD||BC

2 and 5

4 and 7

1

3

2

4

7

5

8

6

D

C

Alternate Int Angles Are Congruent


Parallelograms rectangles rhombi squares

Both Pairs Opp Sides Congruent

X = 23

2Y – 16 = 42

2Y = 58

Y = 29

23

42

2Y - 16

X


Both pairs opposite angles congruent

Both Pairs Opposite Angles Congruent

X = 65

5Y – 5 = 115

5Y = 120

Y = 24

5Y - 5

X

115°

65°


Parallelograms rectangles rhombi squares

Consecutive Angles

Are Supplementary

1

3

2

4

Supplementary angles have a sum of 180


Parallelograms rectangles rhombi squares

Consecutive Angles

Are Supplementary

145˚

x

x = 180 - 145

x = 35˚


Parallelograms rectangles rhombi squares

Diagonals Bisect Each Other

B

C

BX = XD

|

||

X

AX = XC

||

|

A

D


Parallelograms rectangles rhombi squares

Diagonals Bisect Each Other

B

C

25

2x-5

A

D


Parallelograms rectangles rhombi squares

RECTANGLES

Definition

Rectangles Are Parallelograms With 4 Right Angles

All 4 properties About Parallelograms Are True…

PLUS

  • Diagonals are congruent


Parallelograms rectangles rhombi squares

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


Parallelograms rectangles rhombi squares

|

|

|

|

Diagonals Are Congruent

This Gives Us 4 Congruent Segments

And 4 Isosceles Triangles

This Tells Us A Lot About The Angles


Parallelograms rectangles rhombi squares

Diagonals Are Congruent

3x-2

3x-2 = 25

25

3x= 27

x = 9


Parallelograms rectangles rhombi squares

Congruent Pairs of Angles

2

3

4

1

11

9

10

12

8

5

7

6


Parallelograms rectangles rhombi squares

Congruent Pairs of Angles

2

3

4

1

11

9

10

12

8

5

7

6


Parallelograms rectangles rhombi squares

Congruent Pairs of Angles

Find the angle measures

37˚

p

b

a

m

k

s

f

r

h

d

t


Parallelograms rectangles rhombi squares

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


Parallelograms rectangles rhombi squares

4 congruent sides

10

3Y + 1 = 10

3Y = 9

Y = 3

3Y + 1


Parallelograms rectangles rhombi squares

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


Parallelograms rectangles rhombi squares

Diagonals bisect opposite angles

A

B

z

y

y = 50˚

X

z= 30˚

40˚

50˚

D

C


Parallelograms rectangles rhombi squares

SQUARE

The Square Is The Most Special Of All !!

Everything That’s True For

All The Others Is True For Squares.


Parallelograms rectangles rhombi squares

Regular Quadrilateral

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

QUADRILATERALS

PARALLELOGRAMS

RECTANGLES

RHOMBI

SQUARES


Parallelograms rectangles rhombi squares

Quadrilaterals

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


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