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Hierarchy of Polygons
Polygons
Quadrilaterals
Parallelograms Kite
s
Trapezoids
RectangleRhom
bi
Square
Isosceles
Trapezoid
Parallelogram
PROPERTIES REAL LIFE EXAMPLE
Opposite Angles are equal.
Consecutive angles are supplementary .
Diagonals bisect each other.
Opposite sides are congruent.
Rectangle
PROPERTIES REAL LIFE EXAMPLE
Opposite sides are parallel and congruent.
The diagonals bisect each other.
The diagonals are congruent.
Rhombus
PROPERTIES REAL LIFE EXAMPLE
Opposite angle of a rhombus have equal measures.
The diagonals are congruent.
Its diagonals bisect opposite angles. When they bisect each other its at a right angle.
Square
PROPERTIES REAL LIFE EXAMPLE
The diagonals of a square bisect each other and meet at 90 ˚.
Opposite sides are both parallel and equal.
The diagonals of a square bisect its angles and they are also perpendicular.
Diagonals are equal.
Trapezoid
PROPERTIES REAL LIFE EXAMPLE
Quadrilaterals that have one set oppesite sides that are parallel
Isosceles Trapezoid
PROPERTIES REAL LIFE EXAMPLE
Quadrilaterals with one set of opposites are parallel.
Two sides are congruent.
Matrix of Properties
Properties Quads
Opposite angle are equal.
Consecutive angle are supplementary.
Diagonals bisect each other.
Opposite sides are congruent and parallel.
The diagonals are congruent.
Opposite sides of a rhombus have equal measures.
Diagonals bisect opposite angles.
Continued…Diagonals bisect opposite angles.
When they bisect each other is at a right angle.
Diagonals of a square bisect each other and meet at 90 0
Opposite sides are both parallel and equal the diagonals of a square bisect its angles and they are also perpendicular.
Diagonals are equal.
Quadrilaterals that have one set opposite sides that are parallel.
Two sides are congruent.
Proving ParallelogramsIf both pairs of opposite sides are quadrilateral are congruent, then the quadrilateral is a parallelogram.
If both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram.
If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram.
If one pair of opposite sides of a quadrilateral is both parallel and congruent, then the quadrilateral is a parallelogram.
Resources
http://www.learningwave.com/lwonline/geometry_section2/trapezoid/trapezoid1.jpg
http://www.guardianchronicle.com/images/the%20world%20trade%20center.jpg
http://3.bp.blogspot.com/_0gI5te2_CJM/SmlI1KHTuAI/AAAAAAAAABU/g6qV22HceZ0/s400/stewart_graphicrhombusborder.gif
http://library.thinkquest.org/C006354/Pix/2.5.gif
http://www.the-window-treatment-expert.com/images/trapezoid-window.jpg
http://terrystickels.com/db_3squaresto8squares5.jpg
Continued..
Team C006354.(2000). Math Quickie Retrieved April 1, 2011, from http://library.thinkquest.org/C006354/pictures.html&usg=__gyjNkNzwfB16a6zMvAQY-5dPies=&h=162&w=252&sz=20&hl=en&start=1&zoom=1&itbs=1&tbnid=nY47vEppd3aaLM:&tbnh=71&tbnw=111&prev=/images%3Fq%3Dreal%2Blife%2Bexamples%2Bof%2Ba%2Bparallelogram%26hl%3Den%26gbv%3D2%26tbs%3Disch:1&ei=1tSZTcuOEuSV0QHQk9jxCw
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Nicolas Pioch.(2002). Web Museum Retrieved April 1, 2011, from http://www.google.com/imgres?imgurl=http://www.ibiblio.org/wm/paint/auth/malevich/sup/malevich.black-red-square.jpg&imgrefurl=http://www.ibiblio.org/wm/paint/auth/malevich/sup/&usg=__DuxTCba3sY4IwU_nawwDhHPiR-8=&h=1039&w=653&sz=44&hl=en&start=11&zoom=1&itbs=1&tbnid=g2kwBPvAaYggJM:&tbnh=150&tbnw=94&prev=/images%3Fq%3Dsquare%26hl%3Den%26gbv%3D2%26tbs%3Disch:1&ei=_diZTZXHB-Hx0gHyuNSeCg