Thursday, May 11, 2006

Venn Diagram

We can use a venn diagram to help us group the types of quadrilaterals.A venn diagram uses overlapping circles to show relationships between groups of objects. All "quadrilateral" can be separated into three sub-groups: general quadrilaterals, parellelogram, and trapezoid.
Is a rectangle always a rhombus? No, because all four sides of a rectangle don't have to be equal. However, the sets of rectangles and rhombuses do intersect, and their intersection is the set of squares- all squares are both a rectangle and a rhombus.
We can put squares in the intersection of two circles.
Is a trapezoid a parellelogram? No, because a trapezoid has only one pair of parellel sides. That is why we must show the set of trapezoids into a different circle of the diagram.
What about kites? Kites are quadrilaterals that can be parellelograms. If their two pairs of sides are equal, it becomes a rhombus, and if their angles are equal, it becomes a square.

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