1. Dan Krouse, Devon Mazonkey and Feter Peno

2. Hierarchy A hierarchy is a ranking of classes. They show similarities and differences between each class.

3.  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.

5.  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.

6.  Other Properties:  Consecutive angles are supplementary.  If there is one right angle in a parallelogram, then it has four right angles.

8.  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.

9. Rectangles Rectangles have four right angles that are all congruent to each other.

11.  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.

14.  “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.

17.  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.

19.  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.

21.  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.

23.  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.

24. 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/we btexts/geom06.htm http://www.andrews.edu/~calkins/math/we btexts/geom06.htm Jinnan.(2009). Wisdom of the Cloud. Retrieved 3/28/11, from http://Jinnan.com/2009/09/17/the-tao-of- pooh/ http://Jinnan.com/2009/09/17/the-tao-of- pooh/