## Shape Sorter

*and*four congruent angles. Using a Venn diagram, the relationship would look like this:

What other relationships can be described using Venn diagrams? Use this tool to explore many different geometric properties and shapes.

- Begin by selecting the type of Venn diagram that you would like to use.
- Click
one of the
**Select a Rule**drop-down boxes at the bottom of the screen. - Select your rule; an oval will be drawn in the work area.
- If you want to compare
two rules, select a different rule from the other
**Select a Rule**box.

- Click
one of the
- Sort shapes by dragging them from the top menu to the appropriate region of the work area. If you want to preview a shape before moving it, mouse over it and a larger image will appear to the left of the shapes menu.
- When you are done sorting, click the
**Check mark**button to see which shapes are in the correct region and which are not. Correct shapes will be highlighted in**green**with a check mark. Incorrect shapes will be highlighted in**red**with an X. - At any point, you can click the
**Eraser**button to clear all the shapes from the work area. - When you are finished sorting, click
the
**Home**button. This will reset all shapes and rules so you can start your next sorting activity.

Select the rule "All sides are congruent" from the orange Select a rule box and "All angles are congruent" from the green Select a rule box. This will draw two overlapping ovals on your screen called a Venn diagram, creating four regions:

- The orange region is where only the rule "All sides are congruent" applies. Drag one shape from the shapes menu that you think belongs in this region.
- The green region is where only the rule "All angles are congruent" applies. Drag one shape from the shapes menu that you think belongs in this region.
- The orange and green region, where the ovals overlap, is where both rules apply. What statement can you make using mathematical language about this region? Drag one shape from the shapes menu that you think belongs in this region.
- The blue region is where neither rule applies. What statement can you make using mathematical language about the blue region? Drag one shape from the shapes menu that you think belongs in this region.

You should now have four shapes in each of the four regions of your work area. Click the Checkmark button at the bottom to see if you've correctly placed your shapes. If any are incorrect, try to move them to the correct region and find a different shape that might belong in the empty region. Keep checking your answers until all four regions have a shape.

Looking at the shapes in your work area, what do they have in common? How are they different?

Try moving the remaining shapes into the correct region. Check your answers as you work. When you are finished, write some true mathematical statements about your Venn diagram, and then clear the work area and try this activity with two other rules.