Quadrilatarel 4-sided Shapes
Learn about the secrets of quadrilaterals
Meet few of our Shapes
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
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
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.
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