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

Parallelograms are quadrilaterals with Both pairs of opposite sides parallel. ABCD A B CD › › › › › › DEFINITION

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 Alternate Int Angles Are Congruent DC B A AB||DC 1 and 6 3 and 8 AD||BC 2 and 5 4 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 ° X X = 65 5Y – 5 = 115 5Y = 120 Y = 24

Consecutive Angles Are Supplementary Supplementary angles have a sum of 180

Consecutive Angles Are Supplementary 145˚ x x = x = 35˚

Diagonals Bisect Each Other A B C D X || | | BX = XD AX = XC

Diagonals Bisect Each Other A B C D 2x-5 25

Definition Rectangles Are Parallelograms With 4 Right Angles All 4 properties About Parallelograms Are True… PLUS 1)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 | | | |

3x-2 25 Diagonals Are Congruent 3x-2 = 25 3x= 27 x = 9

Congruent Pairs of Angles

Congruent Pairs of Angles

a 37˚ p b h td m f k s r Congruent Pairs of Angles Find the angle measures

Definition A Rhombus Is A Parallelogram With 4 Congruent Sides All 4 properties About Parallelograms Are True… PLUS 1) Diagonals are perpendicular 2) Diagonals bisect opposite angles

4 congruent sides 10 3Y + 1 3Y + 1 = 10 3Y = 9 Y = 3

Diagonal are perpendicular AB CD X 3 4 AB = The perimeter Of rhombus ABCD = XC = DB = Remember the Pythagorean thm.

Diagonals bisect opposite angles AB CD X y 50˚ z 40˚ y = 50˚ z= 30˚

The Square Is The Most Special Of All !! Everything That’s True For Everything That’s True For All The Others Is True For All The Others Is True For Squares.

SQUARE Regular Quadrilateral Regular Parallelogram Equiangular Rhombus Equilateral Rectangle Definitions  Has all the properties of the parallelogram, rectangle and rhombus Equiangular Equilateral Diagonals ≅ & ┴ diagonals bisect each other diagonals bisect opposite <‘s Opposite <‘s ≅ Opposite sides ≅ Consecutive <‘s = 180˚

PARALLELOGRAMS QUADRILATERALS RECTANGLESRHOMBI SQUARES

Parallelograms Both pairs opp. sides of are parallel. Both pairs opp. sides are congruent Both pairs opp. angles are congruent All consecutive angles add to 180. Diagonals bisect each other. One pair of sides is parallel and congruent. Rectangles All four angles are congruent Diagonals are congruent. ALL parallelogram properties. Rhombi All four sides are congruent Diagonals are perpendicular. Opp. angles are bisected. ALL parallelogram properties. Squares The only regular quadrilateral. ALL properties of para, rect, and rhom. I’m thinking of a quadrilateral where all the sides are equal… what could it be? Rhombus or Square I’m thinking of a quadrilateral where the opposite sides are parallel… what could it be? Para, Rect, Rhom, or Square

Parallelograms Both pairs opp. sides of are parallel. Both pairs opp. sides are congruent Both pairs opp. angles are congruent All consecutive angles add to 180. Diagonals bisect each other. One pair of sides is parallel and congruent. Rectangles All four angles are congruent Diagonals are congruent. ALL parallelogram properties. Rhombi All four sides are congruent Diagonals are perpendicular. Opp. angles are bisected. ALL parallelogram properties. Squares The only regular quadrilateral. ALL properties of para, rect, and rhom. Best Name??

Parallelograms Both pairs opp. sides of are parallel. Both pairs opp. sides are congruent Both pairs opp. angles are congruent All consecutive angles add to 180. Diagonals bisect each other. One pair of sides is parallel and congruent. Rectangles All four angles are congruent Diagonals are congruent. ALL parallelogram properties. Rhombi All four sides are congruent Diagonals are perpendicular. Opp. angles are bisected. ALL parallelogram properties. Squares The only regular quadrilateral. ALL properties of para, rect, and rhom.

Parallelograms Both pairs opp. sides of are parallel. Both pairs opp. sides are congruent Both pairs opp. angles are congruent All consecutive angles add to 180. Diagonals bisect each other. One pair of sides is parallel and congruent. Rectangles All four angles are congruent Diagonals are congruent. ALL parallelogram properties. Rhombi All four sides are congruent Diagonals are perpendicular. Opp. angles are bisected. ALL parallelogram properties. Squares The only regular quadrilateral. ALL properties of para, rect, and rhom.

Caution! There is a difference between… What could this be? What’s the best name? It COULD be a parallelogram or a rectangle. All we know FOR SURE is that it is a parallelogram.

Parallelograms Both pairs opp. sides of are parallel. Both pairs opp. sides are congruent Both pairs opp. angles are congruent All consecutive angles add to 180. Diagonals bisect each other. One pair of sides is parallel and congruent. Rectangles All four angles are congruent Diagonals are congruent. ALL parallelogram properties. Rhombi All four sides are congruent Diagonals are perpendicular. Opp. angles are bisected. ALL parallelogram properties. Squares The only regular quadrilateral. ALL properties of para, rect, and rhom.

Quadrilaterals 4 sides, angles add to 360 Parallelograms Opp sides parallel, Opp sides congruent, Opp angles congruent, Consecutive angles =180, Diagonals bisect Rectangle All angles are congruent. Diagonals are congruent. Rhombus All sides are congruent. Diagonals are perpendicular. Opp angles are bisected. Square Everything