# Quadrilatarel 4-sided Shapes

### Learn about the secrets of quadrilaterals

## Meet few of our Shapes

## Properties

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

Diagonals - 5.56

Side angles - 90

Diagonal Vertex angles - 45

Diagonal Angles - 90

## Properties

Diagonals form 2 congruent triangles

Diagonals are perpendicular

## Proof

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

## Properties

· Exactly one pair of opposite sides parallel.

· Exactly one pair of opposite sides congruent.

· Base angles are congruent.

· Diagonals are congruent.

## Measures

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

AD=9.94

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

## 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.

## Proof

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<EAD=37.39

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<BAD=74.77

M<ADC=105.23

M<DCB=74.77

BA=8.66

AD=8.65

## 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<ADE=18.49

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

m<EAD=14.08

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