1 / 24

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.

kipp
Télécharger la présentation

Quadrilaterals

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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/

More Related