## Background Info

Be prepared to learn them!

## Square

A square is a quadrilateral with four right angles and four congruent sides. In the exercises, you will show that a square is a parallelogram, a rectangle, and a rhombus. So a square has the properties of all three.

## Properties

All base angles are congruent.
Both pairs of opposite sides are congruent.
Both pairs of opposite sides are parallel to each other.
Diagonals are perpendicular.
Diagonals are congruent.
Both pairs of opposite angles are congruent.
Diagonals bisect the angles.
Diagonals form two isosceles triangles.
All angles are congruent.
All sides are congruent.
Diagonals bisect each other.

## Proof

Sides- 4

Diagonals - 5.56

Side angles - 90

Diagonal Vertex angles - 45

Diagonal Angles - 90

## Kite

A kite is a quadrilateral with exactly two pairs of congruent consecutive sides.

## Properties

Diagonals form 2 congruent triangles

Diagonals are perpendicular

ANGLES FOR KITE

m<UWV=101.1

m<UWY=39.12

m<YWV=61.98

m<WVX=55.78

m<WVY=27.85

m<YVX=27.93

m<UXV=101.67

m<YXV=62.24

m<UXY=39.43

m<XUW=101.45

m<XUY=50.96

m<YUW=50.5

m<WYU=90.39

m<WYV=90.17

m<VYX=89.83

m<XYU=89.61

Sides for Kite

UV=6.48 cm

WV=5.13cm

UW=3.1cm

UX=3.08cm

XV=5.11cm

WX=4.79cm

YW=2.39cm

YX=2.39cm

YV=4.52cm

YU=1.96cm

## Properties

Both pairs of opposite sides are parallel

Both pairs of opposite sides are congruent

Opposite angles are congruent

All angles are congruent

Diagonals form 2 congruent triangles

Diagonals are congruent

Diagonals bisect each other

Base angles are congruent

## Proof

ANGLES FOR RECTANGLE

m<CDE=90

m<DCA=90

m<CAB=90

m<ABD=90

m<CDE=22.21

m<EDB=67.79

m<DBE=67.79

m<EBA=22.21

m<EAB=22.21

m<EAC=67.79

m<ACE=67.79

m<ECD=22.21

m<CED=135.57

m<DEB=44.43

m<BEA=135.57

m<AEC=44.43

SIDE FOR RECTANGLE

ED=5.69 cm

EB=5.69 cm

CB=11.37 cm

DC=10.53 cm

AB=10.53 cm

CA=4.3 cm

BD=4.3 cm

EA=5.69 cm

CE=5.69 cm

DA=11.37 cm

## Trapazoid

A trapezoid is a quadrilateral with exactly one pair of parallel sides. Each of the parallel sides is called a base . The nonparallel sides are called legs . Base angles of a trapezoid are two consecutive angles whose common side is a base. If the legs of a trapezoid are congruent, the trapezoid is an isosceles trapezoid. The following theorems state the properties of an isosceles trapezoid.

## Properties

· Exactly one pair of opposite sides parallel.

· Exactly one pair of opposite sides congruent.

· Base angles are congruent.

· Diagonals are congruent.

M<ACD=117.79

M<CAB=122.94

M<CDB=62.21

M<ABD=57.06

AC=6.48

AB=5.37

CD=5.09

DB=11.78

CB=10.42

EB=6.72

CE=3.70

ED=6.41

AE=3.53

M<DEB=127.45

M<EBD=25.60

M<BDE=26.95

M<VED=52.55

M<EDC=35.26

M<DCE=92.19

M<AEB=52.55

M<EAB=95.98

M<ABE=31.47

M<CEA=127.45

M<ACE=25.60

M<CAE=26.95

## Rhombus

A rhombus is another special quadrilateral. A rhombus is a quadrilateral with four congruent sides.

Like a rectangle, a rhombus is a parallelogram. So you can apply the properties of parallelograms to rhombuses.

## Properties

Both pairs of opposite sides parallel.

· Both pairs of opposite sides congruent.

· All sides congruent.

· Diagonal forms 2 congruent triangles.

· Diagonal forms 2 congruent isosceles triangles.

· Diagonals bisect the opposite angles.

· Diagonals are perpendicular.

· Diagonals bisect each other.

M<CBE=52.61

M<BEC=90

M<ECB=37.39

M<BEA=90

M<EAB=37.39

M<EBA=52.61

M<AED=90

M<EDA=52.61

M<CED=90

M<EDC=52.61

M<ECD=37.39

DB=10.51

BE=5.26

DE=5.26

AC=13.76

AE=6.88

CE=6.88

M<CBA=105.23

M<DCB=74.77

BA=8.66

## Properties

Both pairs of opposite sides are parallel

Both pairs of opposite sides are congruent

Opposite angles are congruent

Diagonals form 2 congruent triangles

Diagonals bisect each other

## Proof

ANGLES FOR PARALLELOGRAM

m<BAC=49.43

m<DBA=98

m<CDB=98

m<DAC=14.08

m<EDC=98

m<ECD=49.43

m<ECB=14.08

m<EBC=18.49

m<EBA=98

m<EAB=49.43

m<DEC=32.57

m<CEB=147.43

m<BEA=32.57

m<AED=147.43

SIDES FOR PARALLELOGRAM

EC=9.75 CM

ED=7.48 CM

AE=9.75 CM

BE=7.48 CM

CD=5.3 CM

AC=19.5 CM

BD=14.96 CM

BC=16.55 CM

BA=5.3 CM

DA=16.55 CM