Emily Gray
12/3/2011
Exploring Quads
Title
Exploring Quadrilaterals
Problem Statement
Exploring Quadrilaterals
Use Sketchpad to construct the following quadrilaterals. Be sure your quadrilateral is
constructed so that when you drag on a vertex, the properties of the quadrilateral are
maintained.
Use the document option of Sketchpad to construct each quadrilateral on a separate page.
Name each page by the name of the quadrilateral.
parallelogram that is not a rectangle
rectangle
rhombus that is not a square
square
trapezoid
kite that is not a rhombus
Investigate the properties of each quadrilateral. For ex., how are the lengths of the sides
related? How are the angles related? What do you notice about the diagonals?
Summarize your findings for each quadrilateral in a Word document. Save this document
and your GSP file to your Class Docs folder.
Problem Setup
Construct each quadrilateral. Compare and contrast the properties of each quadrilateral
according to length of sides, angles, and diagonals. This is very similar to the Mystery
Quadrilaterals Problems except we are not given the shape to start with. We must
construct the shapes ourselves.
Investigation
I began by constructing each shape using GSP and following the properties that I had
learned for each shape making sure to measure off angles and lengths. I then printed each
shape out and used colored pens to mark congruencies. Any angles, sides, or diagonals
that were congruent on a quadrilateral were given the same color. I then went through
each shape and made notes about what was similar and what was not and the number of
similarities.
Parallelogram that is not a Rectangle
Two pairs of vertical congruent sides
Diagonals bisect each other
Two pair of vertical interior angles
Two pair of vertical interior angles around the center point where diagonals
intersect
Rectangle
Four right angles at each vertex
Two pairs of congruent opposite sides
Diagonals bisect each other
Congruent alternate interior angles around center point
Emily Gray
12/3/2011
Exploring Quads
Rhombus that is not a square
All sides congruent
Congruent opposite angles at each vertex
Congruent/right angles around the center point
Diagonals bisect each other
Two pair of congruent vertical interior angles
Square
All right angles at each vertex
Right angles around center point
Diagonals bisect each other and congruent
All sides congruent
Trapezoid
One pair of parallel lines
Kite that is not a Rhombus
Two pair of adjacent congruent sides
Angles around center point congruent/right
Diagonals bisect angles at each vertex
Extensions of the problem
None
Author & Contact
Emily Gray
Egray2@aug.edu