dan krouse, devon mazonkey and feter peno. hierarchy a hierarchy is a ranking of classes. they show...
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QUADRILATERALS Dan Krouse, Devon Mazonkey and
Feter Peno
HierarchyA hierarchy is a ranking of classes.They show similarities and differences between each class.
Diagonals
A diagonal is a segment connecting two non-consecutive vertices.
Many polygons can have several diagonals.
All quadrilaterals have four sides which means they all have two diagonals.
Diagonals
Parallelogram
A parallelogram is a quadrilateral with opposite sides that are parallel.
Properties: Opposite sides are always congruent Opposite angles are congruent as well Back to diagonals, the diagonals always bisect
each other. Each diagonal forms two congruent triangles.
Parallelograms
Other Properties: Consecutive angles are supplementary. If there is one right angle in a parallelogram,
then it has four right angles.
Parallelogram
Rectangles
A rectangle is very closely related to a parallelogram.
The most common difference is that the diagonals are congruent in rectangles.
There are five properties of a rectangle, but there is only one different from a parallelogram. That is: Diagonals are congruent and bisect each
other.
RectanglesRectangles have four right angles that are all congruent to each other.
Rhombuses or Rhombi?
A rhombus is a special kind of square. It is a quadrilateral with all four sides
congruent. The properties of a parallelogram are
applied to a rhombus. Although, some new properties are:
The diagonals are perpendicular. Each diagonal bisects a pair of opposite
angles.
Rhombi
Squares
“Are you a square, get it? Ahhh.” –Pete The square is a little bit tricky, it is a
rectangle, a rhombus. Also, to top it off, it has the properties of
a rectangle, a rhombus, and a parallelogram.
Squares
Squares
Kites
A kite is two disjoint pairs of congruent adjacent sides.
When the diagonals are present, they form two congruent triangles.
The two diagonals in a kite are perpendicular, therefore they form four right angles.
Kites
Trapezoids
A trapezoid is a quadrilateral with two bases that are parallel and two legs.
The two legs cannot be parallel but can be congruent.
The base’s angles are formed by a base and one leg.
One new definition is median which is a segment that joins two midpoints.
Trapezoids
Isosceles Trapezoid
An isosceles trapezoid is very much like a trapezoid, but the legs are congruent is an isosceles trapezoid.
Some Properties of an Isosceles Trapezoid are: The base angles are always congruent. The diagonals are always congruent as well. Also, the median splits the legs into two
congruent lengths.
Isosceles Trapezoids
Real Life Examples
Our real life examples are shown in many of the previous slides, such as the squares, trapezoids, and isosceles trapezoids.
They show the properties of all similarities of quadrilaterals to form structures or buildings.
References
Boyd, C., Cummins, J., Malloy, C., Carter, J., Flores, A.(2005). Geometry (pp.402-452). Columbus, Ohio: McGraw-Hill Inc.
Calkins, K.(2005). Classifying Polygons by Symmetry. Retrieved 3/24/11, from http://www.andrews.edu/~calkins/math/webtexts/geom06.htm
Jinnan.(2009). Wisdom of the Cloud. Retrieved 3/28/11, from http://Jinnan.com/2009/09/17/the-tao-of-pooh/