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**Polygons and Venn Diagrams**

A GEMS/ALEX Submission as part of a larger lesson “Relationships of Polygons: An in-depth investigation to foster mathematical thinking “ Submitted by: Elizabeth Thompson, PhD. Summer, 2008

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**Polygons 2 9 14 20 27 35 Name Number of sides/angles and vertices**

Diagonals Triangle 3 Polygon 4 2 Pentagon 5 Hexagon 6 9 Heptagon 7 14 Octagon 8 20 Nonagon 27 Decagon 10 35 Give drawn example of a polygon and its diagonals. Have students identify the pattern for the diagonals ( ….etc…)

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**Venn Diagrams – a sample**

Boys Class Girls Let the students make some sample with you in class on the board.

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**Assignment: Create a Venn Diagram using the four sided polygons & their characteristics**

A parallelogram has two parallel pairs of opposite sides. A rectangle has two pairs of opposite sides parallel, and four right angles. It is also a parallelogram, since it has two pairs of parallel sides. A square has two pairs of parallel sides, four right angles, and all four sides are equal. It is also a rectangle and a parallelogram. A rhombus is defined as a parallelogram with four equal sides. Is a rhombus always a rectangle? No, because a rhombus does not have to have 4 right angles. Trapezoids only have one pair of parallel sides. It is not a parallelogram. Kites- two pairs of adjacent sides that are equal. Keep this up while students work on their Venn Diagrams and/or print one slide and assign as Homework/Lab assignment on Paint.

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**The next slide will have a solution to the Venn Diagram Assignment.**

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**Solution All Quadrilaterals Parallelograms Trapezoids Rhombus Squares**

rectangles Click for Kite placement. If you like you can work on this with the students by having object ‘fly-in’…simply reformat the PowerPoint. Kites can be a rhombus or a square, but are not parallelograms…its hard to place the kite. What about Kites???

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PinpointingProperties. Trapezoids Make these trapezoids on your geoboard. How many sides? How many angles? Are any sides congruent? No sides are congruent.

PinpointingProperties. Trapezoids Make these trapezoids on your geoboard. How many sides? How many angles? Are any sides congruent? No sides are congruent.

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