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Quadrilaterals

Quadrilaterals . Dan Krouse , Devon Mazonkey and Feter Peno. Hierarchy. A 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.

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Quadrilaterals

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  1. Quadrilaterals Dan Krouse, Devon Mazonkey and FeterPeno

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

  3. 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.

  4. Diagonals

  5. 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.

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

  7. Parallelogram

  8. 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.

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

  10. Rectangles

  11. 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.

  12. Rhombuses or Rhombi?

  13. Rhombi

  14. 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.

  15. Squares

  16. Squares

  17. 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.

  18. Kites

  19. 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.

  20. Trapezoids

  21. 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.

  22. Isosceles Trapezoids

  23. 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.

  24. 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/

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