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Hierarchy of Quadrilaterals

A visualization of the hierarchy of Quadrilaterals
by

Patricia Alonso

on 12 April 2013

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Transcript of Hierarchy of Quadrilaterals

Quadrilaterals Parallelograms Parallelogram- a four sided, closed shape with opposite sides parallel(math word definition).
Sides: two sets of parallel sides, two sets of congruent sides
Angles: opposite angles are congruent, and any pair of consecutive angles add up to 180 degrees (Supplementary Angles)
Diagonals: the diagonals intersect, but does not have right angles.
(Properties of Quadrilaterals) Trapezoids Hierarchical Structure of Quadrilaterals Kites Rectangles Rhombuses Squares Kite- has two disjoint pairs of consecutive sides that are congruent.
Sides: disjoint pairs of consecutive sides are congruent.
Angles: one set of congruent angles. They are opposite from each other and are between sides of different lengths.
Diagonals: form right angles and are perpendicular (Properties of Quadrilaterals).
Relationship: A kite is not a parallelogram because it does not have two sets of parallel lines. It is not a trapezoid because the angles are all the same rather than transversal. Rectangle: the opposite sides must be congruent and the opposite sides need to be parallel.
Sides: opposite sides are congruent and parallel
Angles: in the rectangle make 90 degree angles. Diagonals: are congruent and the length of a diagonal can be found with the pythagoreom theorem.
Relationship: a rectangle is considered a parallelogram because it has two sets of parallel sides. Rhombus- a special type of parallelogram where all four sides are the same length(math word definition).
Sides: all four sides are congruent
Angles: any pair of consecutive angles are supplementary angles
Diagonals: bisect the angles, are perpendicular bisectors of each other, and divide the rhombus into four congruent right triangles
(Properties of Quadrilaterals). Square- a four sided, closed figure with four congruent sides and four interior right angles(math word definition).
Sides: all four sides are congruent
Angles: all interior angles are 90 degrees
Diagonals: form four isosceles right triangles
(Properties of Quadrilaterals) Patricia Alonso and Barbara Martinez-Romero Quadrilateral: a closed, four-sided shape with angles that add up to 360 degrees. The sides do not have to all be congruent. It is the parent of all the figures below.
Trapezoids- a four sided shape with at least one pair of parallel sides.
Sides: opposite sides that are parallel. These sides are referred to as the bases while the non-parallel sides are called legs.
Angles: no angles need to be congruent Diagonals: are transversals
Relationship: A trapezoid is not a parallelogram because it does not have two sets of parallel sides. Works Cited "Kite." , Angles, Sides, Diagonals. N.p., n.d. Web. 08 Apr. 2013. <http://www.mathwarehouse.com/geometry/quadrilaterals/kite.php>.

"The Properties of a Kite." Cool Math .com - The Properties of a Kite (perimeter, Area, Interior Angles, Diagonals, Lengths of Sides). N.p., n.d. Web. 08 Apr. 2013. <http://www.coolmath.com/reference/kites.html>.

"The Properties of a Rectangle." The Properties of a Rectangle (perimeter, Area, Interior Angles, Diagonals, Lengths of Sides). N.p., n.d. Web. 08 Apr. 2013. <http://www.coolmath.com/reference/rectangles.html>.

"The Properties of a Trapezoid." The Properties of a Trapezoid (perimeter, Area, Interior Angles, Diagonals, Lengths of Sides). N.p., 2012. Web. 08 Apr. 2013. <http://www.coolmath.com/reference/trapezoids.html>.

"Rectangle: Shape and Properties." Rectangle Sides, Diagonals, and Angles. N.p., n.d. Web. 08 Apr. 2013. <http://www.mathwarehouse.com/geometry/quadrilaterals/parallelograms/rectangle.php>.

Ryan, Mark. "The Properties of a Kite." For Dummies. N.p., n.d. Web. 08 Apr. 2013. <http://www.dummies.com/how-to/content/the-properties-of-a-kite.html>.

"Trapezoid." Bases, Legs, Angles and Area, The Rules and Formulas. N.p., n.d. Web. 08 Apr. 2013. <http://www.mathwarehouse.com/geometry/quadrilaterals/trapezoid.php>.

"Trapezoid." Trapezoid. N.p., 2012. Web. 08 Apr. 2013. <http://www.mathsisfun.com/geometry/trapezoid.html>.
"Trapezoids." Trapezoids. N.p., n.d. Web. 08 Apr. 2013. <http://www.math.washington.edu/~king/coursedir/m444a00/syl/class/trapezoids/Trapezoids.html>.

"PROPERTIES OF QUADRILATERALS." N.p., n.d. Web. 12 Apr. 2013. <http://www.lavcmath.com/shin/quadrilaterals.pdf>.

Recycled prezi format by Jeremy Loughheed

"Square - Math Word Definition - Math Open Reference." Square - Math Word Definition - Math Open Reference. N.p., n.d. Web. 12 Apr. 2013. <http://www.mathopenref.com/square.html>. Relationship: a parallelogram is not a trapezoid because it has more than one set of parallel sides. It is not a kite because it has two sets of parallel sides. Relationship:This quadrilaterral is similar to the square but since it does not have right angles,it is not a square. (only the diagonals make right angles) Relationship: This quadrilateral is similar to the trapezoid but since it has all sides congruent and right angles, it is not a trapezoid.
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