QuadrilateralsSara BebermanOlivia DeFlumeri

Olivia HuynhAmanda Okaka

Parallelogram•A parallelogram is a quadrilateral with both pairs of opposite sides parallel

- if a quadrilateral has two pairs of opposite sides congruent then it is a parallelogram ex: (AB DC)≅-if a quadrilateral has two pairs of opposite angles congruent

then it is a parallelogram ex:(<DAB <DCB)≅-if a quadrilateral has one pair of opposite sides congruent and parallel then it is a parallelogram ex: (AD BC and ADllBC)≅-if a quadrilateral has diagonals that bisect each other then it is

a parallelogram ex: (AE EC and DE EB)≅ ≅

Parallelogram

• Properties of a parallelogram:

-opposite sides are congruent (AB DC)≅-opposite angles are congruent (<ADC <ABC)≅-consecutive angles are supplementary (<DAB + <ABC= 180°)

-diagonals bisect each other (AC bisects BD)

KITE PROPERTIESTwo sets of adjacent sides are congruentOne set of congruent angles opposite each otherDiagonals are perpendicularThe longer diagonal of the kite bisects the shorter diagonal

-A quadrilateral with two distinct pairs of congruent adjacent sides.

A

B

C

D

•AB≅AD, DC≅BC, (Two sets of congruent adjacent sides)•AE is perpendicular to DB•DE≅EB (The longer diagonal bisects the shorter diagonal)•<ADC≅<ABC (One set of angles congruent)

E

Rhombus

Rhombus: a parallelogram with a pair of congruent adjacent sides

Properties: Opposite sides are congruent and parallel AB BC CD DA

AB // CD and BC // DA Opposite angles are congruent

ABC ADC and BAD BCD Consecutive angles are supplementary

BAD + ABC = 180 and ADC + DCB = 180BAD + ADC = 180 and ABC + DCB =180

Diagonals bisect each otherBO DO and AO CO

Diagonals are perpendicularAOB = BOC = COD = DOA = 90

The diagonals bisect the anglesBAC DAC, ABD CBD, BCA DCA, and CDB ADB

 

Trapezoid

Trapezoid: A quadrilateral, which has only one set of opposite sides parallel Properties: Exactly one pair of opposite sides is parallel

BC//AD Consecutive angles on different bases are supplementary

DAB + ABC = 180 and ADC + BCD = 180

Rectangle

• Definition – A rectangle is a parallelogram that has four right angles, 2 sets of opposite sides congruent, and congruent diagonals

•Properties of a Rectangle• both pairs of opposite sides are congruent and

parallel

• diagonals are congruent

• diagonals bisect one another

• consecutive angles are supplementary

• both pairs of opposite angles are congruent

• has 4 right anglesEx. * AB is Congruent and Parallel to DC, AD is Congruent and Parallel to BC

* Diagonal X and Diagonal Y are Congruent and bisect one another

* <A + <D = 180˚, <B + <C = 180˚, <A + <B = 180˚, <D + <C = 180˚

•<A ≅ <C, <B ≅ <D

• <A, <B, <C, and <D are all right angles (each equal 90˚)

A B

CD

X Y

Square

* Definition – A parallelogram with all right angles and all side lengths congruent

• Properties of a Square:

• All sides are congruent

• Opposite sides are parallel

• All angles are congruent (all right angles)

• Consecutive angles are supplementary

• Diagonals are congruent

• Diagonals are perpendicular

• Diagonals bisect one another

• Diagonals bisect the angles

Ex.

•AB is congruent to BC is congruent to CD is congruent to AD

•AB is parallel to DC, AD is parallel to BC

•<A, <B, <C, <D are all right angles (all congruent)

•<ABC + <BCD = 180°

•BD = AC

•AC is perpendicular to BD

•AC bisects BD, BD bisects AC

•BD bisects <ABC and <ADC, AC bisects <BAD, <BCD

A square is both a rectangle and a rhombus.