## Properties of Polygons: When Students Ask

• Why do I need to know about plane figures?
Geometry helps students represent and describe the world in an orderly manner. Plane geometry helps students represent and describe figures on a flat surface. Geometric ideas are often used to help solve problems or represent ideas in other areas of mathematics. For example, rectangles can be used to model fractions, and the concepts of circles and central angles are used to display data in circle graphs. Geometric ideas are also useful in other fields of study such as architecture, designs, art, and geography.
• How do I use a protractor?
Many students have problems using a protractor. When they measure angles, make sure students place the center of the protractor on the vertex of the angle and align one of the rays of the angle with the zero degree mark on the protractor. Also make sure students read the angle measure from the correct scale on the protractor. Thinking about whether the angle is greater than or less than 90 degrees before they measure it will help students choose the correct measure.
• What's the difference between similar and congruent figures?
Congruent figures have exactly the same shape and size, whereas similar figures need only have the same shape. To help students understand similarity, give real-world examples of similar figures. For instance, the negative of a picture and the picture itself are similar. The picture has the same shapes as the negative, but they are usually larger than the shapes in the negative. A drawing placed on an overhead projector and its projected image are also similar. For figures to be similar, corresponding angles must be congruent and corresponding sides must be proportional. For example, a rectangle whose side lengths are 3 cm and 5 cm is similar to a rectangle whose side lengths are 9 cm and 15 cm, because corresponding angles are congruent and the ratio of corresponding sides is 1 to 3.
• What should I know about transformations?
Students should know that translations, reflections, and rotations are transformations that result in congruent images. A translation can be thought of as a slide in one direction by a certain distance. A rotation is a turn about a point. The point about which the figure is turned may or may not be on the figure. A reflection is a flip over a line. A reflection changes the orientation of the figure, creating a mirror image of the figure. Translations, reflections, and rotations are often used in designs for floors, murals, and wallpaper.