SECTION 8-2, 8-4, 8-5SECTION 8-2, 8-4, 8-5 spi.3.2.Hspi.3.2.H

Jim Smith JCHSJim Smith JCHS

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

ABCDABCDAA BB

CCDD

››

››

›››› ››››

5 Things About Parallelograms5 Things About Parallelograms

DefinitionDefinition1) Both Pairs Opp Sides 1) Both Pairs Opp Sides ParallelParallel

PropertiesProperties2) Both Pairs Opp Sides 2) Both Pairs Opp Sides CongruentCongruent

3) Both Pairs Opp Angles 3) Both Pairs Opp Angles CongruentCongruent

4) Consecutive Angles 4) Consecutive Angles SupplementarySupplementary

5) Diagonals Bisect Each 5) Diagonals Bisect Each OtherOther

Both Pairs Opp Sides ParallelBoth Pairs Opp Sides Parallel

Alternate Int Angles Are CongruentAlternate Int Angles Are Congruent

1122

3344

5566

7788

DD CC

BBAAAB||DCAB||DC1 and 61 and 63 and 83 and 8

AD||BCAD||BC2 and 52 and 54 and 74 and 7

Both Pairs Opp Sides CongruentBoth Pairs Opp Sides Congruent

2323

XX

4242 2Y - 162Y - 16

X = 23X = 232Y – 16 = 422Y – 16 = 42 2Y = 582Y = 58 Y = 29Y = 29

Both Pairs Both Pairs OppositeOpposite Angles CongruentAngles Congruent

65°65°

5Y - 55Y - 5

115°115°

XX X = 65X = 65

5Y – 5 = 1155Y – 5 = 115 5Y = 1205Y = 120 Y = 24Y = 24

Consecutive AnglesConsecutive AnglesAre SupplementaryAre Supplementary

11

22

33

44

Supplementary angles have a sum of 180

Diagonals Bisect Each OtherDiagonals Bisect Each Other

AA

BB CC

DD

XX ||||||

||||||

BX = BX = XDXDAX = AX = XCXC

Rectangles Are Rectangles Are Parallelograms With 4 Parallelograms With 4

Right AnglesRight Angles

All 5 Things About All 5 Things About ParallelogramsParallelogramsAre True…Are True…PLUSPLUS

1)1) All angles = 90°All angles = 90°2)2) Diagonals are congruentDiagonals are congruent

All Angles = 90°All Angles = 90°

If 1 Angle In A Parallelogram Is A If 1 Angle In A Parallelogram Is A RightRight

Angle, Then All 4 Angles Are Right Angle, Then All 4 Angles Are Right AnglesAngles

This gives usThis gives usright triangles alsoright triangles also

Diagonals Are CongruentDiagonals Are Congruent

This Gives Us 4 Congruent SegmentsThis Gives Us 4 Congruent SegmentsAnd 4 Isosceles TrianglesAnd 4 Isosceles Triangles

This Tells Us A Lot About The AnglesThis Tells Us A Lot About The Angles

||

||

||

||

1122 33

44

556677

1111

1212101099

88

Congruent Pairs of AnglesCongruent Pairs of Angles

1122 33

44

556677

1111

1212101099

88

Congruent Pairs of AnglesCongruent Pairs of Angles

A Rhombus Is A A Rhombus Is A Parallelogram WithParallelogram With4 Congruent Sides4 Congruent SidesAll 5 Things About All 5 Things About

Parallelograms Are True…Parallelograms Are True…PLUSPLUS

1)1) 4 congruent sides4 congruent sides2)2) Diagonal are Diagonal are perpendicularperpendicular

3)3) Diagonals bisect Diagonals bisect opposite anglesopposite angles

4 congruent sides4 congruent sides

1010

3Y + 13Y + 1

3Y + 1 = 103Y + 1 = 10 3Y = 93Y = 9 Y = 3Y = 3

Diagonal are perpendicularDiagonal are perpendicularAA BB

CCDD

XX33 44

AB = The perimeter Ofrhombus ABCD =

XC = DB =

55

20203388

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.

PARALLELOGRAMSPARALLELOGRAMS

QUADRILATERALSQUADRILATERALS

RECTANGLESRECTANGLES RHOMBIRHOMBI

SQUARESSQUARES