HOMEWORK:5.5/1-6, 9-11,16, 175.6/1-13, 28

Parallelograms are quadrilaterals withParallelograms are quadrilaterals withBoth pairs of opposite sides parallel. Both pairs of opposite sides parallel.

ABCDABCDAA BB

CCDD

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DEFINITION

4 Properties of Parallelograms

Definition Quadrilateral with both pairs

opposite sides parallel

Properties1) Both Pairs Opp Sides Congruent2) Both Pairs Opp Angles Congruent3) Consecutive Angles Supplementary4) Diagonals Bisect Each Other

Both Pairs Opp Sides Parallel

Alternate Int Angles Are Congruent

12

34

56

78

D C

BAAB||DC1 and 63 and 8

AD||BC2 and 54 and 7

Add a transversal and ..

Both Pairs Opp Sides Congruent

23

X

42 2Y - 16

X = 23

2Y – 16 = 42 2Y = 58 Y = 29

Both Pairs Opposite Angles Congruent

65°

5Y - 5

115°

X X = 65

5Y – 5 = 115 5Y = 120 Y = 24

Consecutive AnglesConsecutive AnglesAre SupplementaryAre Supplementary

11

22

33

44

Supplementary angles have a sum of 180

Consecutive AnglesAre Supplementary

145˚

x

x = 180 - 145x = 35˚

Diagonals Bisect Each Other

A

B C

D

X |||

|||

BX = XDAX = XC

Diagonals Bisect Each OtherDiagonals Bisect Each Other

AA

BB CC

DD2x-

5

25

DefinitionRectangles Are

Parallelograms With 4 Right Angles

All 4 properties About Parallelograms Are True…

PLUS1)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 usright triangles also

Diagonals Are Congruent

This Gives Us 4 Congruent SegmentsAnd 4 Isosceles Triangles

This Tells Us A Lot About The Angles

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|

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3x-225

Diagonals Are Congruent

3x-2 = 253x= 27

x = 9

1122 33

44

556677

1111

1212101099

88

Congruent Pairs of Angles

12 3

4

567

11

12109

8

Congruent Pairs of Angles

a37˚ p

b

htd

m

fks

r

Congruent Pairs of AnglesFind the angle measures

DefinitionA Rhombus Is A

Parallelogram With4 Congruent Sides

All 4 properties About Parallelograms Are True…

PLUS1) Diagonals are perpendicular

2) Diagonals bisect opposite angles

4 congruent sides

10

3Y + 1

3Y + 1 = 10 3Y = 9 Y = 3

Diagonal are perpendicularA B

CD

X3 4 AB =

The perimeter Ofrhombus ABCD =

XC = DB =

5

2038

Remember the Pythagorean

thm.

Diagonals bisect opposite anglesA B

CD

X

y

50˚

z

40˚

y = 50˚

z= 30˚

The Square Is The The Square Is The Most Special Of All !!Most Special Of All !!

Everything That’s Everything That’s True ForTrue For

All The Others Is True All The Others Is True

For For Squares.

SQUARERegular Quadrilateral

Regular Parallelogram

Equiangular Rhombus

Equilateral Rectangle

Definitions

Has all the properties of

the parallelogram, rectangle and

rhombus

EquiangularEquilateral

Diagonals ≅ & ┴diagonals bisect each other diagonals bisect opposite

<‘sOpposite <‘s ≅

Opposite sides ≅Consecutive <‘s = 180˚

PARALLELOGRAMSPARALLELOGRAMS

QUADRILATERALSQUADRILATERALS

RECTANGLESRECTANGLES RHOMBIRHOMBI

SQUARESSQUARES

Quadrilaterals4 sides, angles add to 360

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

Consecutive angles =180, Diagonals bisect

RectangleAll angles are congruent.Diagonals are congruent.

RhombusAll sides are congruent.Diagonals are perpendicular.Opp angles are bisected.

SquareEverything