When people hear the word geometry, they tend to think about shapes. These shapes surround their lives each and every day. Many of these shapes, or **polygons**, can be described as flat closed figures with 3 or more sides. Polygons are two-dimensional objects, not solids. Polygons are classified and described by the number of sides, the kind of angles, and whether any of the sides are the same length (or **congruent**). Many polygons have special names.

This figure shows the most common polygons. Notice that we identified a 4-sided polygon as a quadrilateral. More commonly, you'd call this shape a rectangle, but a rectangle is only one kind of quadrilateral. A rectangle is a special quadrilateral where opposite sides are **congruent** -- that is, the same length -- and each angle is a right angle. A square is also a special quadrilateral because all four sides are congruent and all four angles are right angles. Notice the similarities between rectangles and squares:

- They both are quadrilaterals (four sided polygons).
- Opposite sides are congruent for squares and rectangles.
- All four angles are right angles for both.

The one important difference is that all four sides are congruent for a square. You could put it this way: All squares are rectangles, but not all rectangles are squares.

Triangles have their own special cases as well. An **equilateral** triangle can be thought of as the square's cousin since all three sides are congruent. Another special triangle is the **isosceles** triangle, where only two sides are congruent. A **scalene** triangle has no congruent sides.

## Introducing the Concept

Since much of the vocabulary for polygons will be new to your students, it is a good idea to begin by spending a day making connections between objects in your classroom and the new vocabulary. This will allow you to tie what the students are learning to real-life examples of polygons.

**Materials**: Colored poster paper, straight edge, and scissors.

**Preparation**: Cut out the following polygons and post them. Make sure that they are large enough for the entire class to see. Use different colors for each polygon and write the name of each in the center of the cut-out.

**Prerequisite Skills and Concepts**: Students should know about triangles and rectangles and basic properties of these shapes such as the number of sides of each.

**Ask**: (While pointing at the triangle)*What shape is this?*(triangle)*Can anyone tell me what makes a triangle different from other shapes?*

Students should identify that a triangle has three sides. Some may also say that it has three angles. Write these properties below the shape on the board.**Ask**: (Write the word tricycle on the board)*How many of you had a tricycle when you were little boys and girls?**How many wheels does a tricycle have?**What do a tricycle and a triangle have in common?*

When students identify that a tricycle has three wheels and a triangle has three sides, make the connection between the prefix*tri-*and the number three.- Below the properties of the triangle, write "Tri means 3."
**Ask**: (While pointing at the quadrilateral)*This shape is called a quadrilateral. What can you tell me about it?*

Students should identify that a quadrilateral has four sides. Some may also say that it has four angles. Write these properties below the shape on the board.- Continue by explaining that
*quad-*means*four*. Then write "quad means 4" below the quadrilateral. **Ask**: (While pointing at the pentagon)*This is a pentagon. What can you tell me about it?*

Again, students should identify the number of sides and possibly angles for a pentagon.**Ask**:*Who knows what prefix means five in the word pentagon?*

Some students may also beat you to the punch line by informing you that*pent-*means five before you ask this question.- Continue for the hexagon and octagon. Some students will be thinking ahead and already have the prefixes for 6 and 8.

## Developing the Concept

Once your students can identify different polygons, move on to identifying properties of specific polygons. This is also the time to make sure that your students know and use the correct mathematical vocabulary when describing properties of polygons.

**Materials**: Student worksheets 1 and 2, overhead projector, ruler for each student or for pairs of students, ruler to use on overhead

**Preparation**: Prepare an overhead transparency of worksheets 1 and 2. Distribute the student worksheets to each child.

**Ask**:*We have talked about different kinds of polygons. How did we describe a triangle?*

List the properties of a triangle on the board: Three-sided polygon, contains three angles or corners.**Say**:*Look at worksheet 1. All these figures are triangles, but some of them have special names. Look at figure c. Use your ruler to measure the three sides of this triangle.*

Demonstrate using your own ruler on the transparency.**Ask**:*Are all three sides the same length?*(yes)**Say**:*A triangle that has all the sides the same length is called an***equilateral**triangle. Look at the worksheet. Are any of the other triangles equilateral? Use your ruler to check.

Allow plenty of time for students to measure, then ask for volunteers. Figure e is also equilateral.**Ask**:*Did anyone think that Figure a was equilateral?*

Explain that Figure a has two sides that are the same length, but the third side is a different length.**Say**:*A triangle with two equal sides is called an***isosceles**triangle. Are there any other isosceles triangles on the worksheet? Use your ruler to check.**Say**:*Figure f is isosceles.*

Make sure students are clear on the difference between isosceles and equilateral triangles.**Say**:*Look at the other triangles on the worksheet. These triangles have sides that are all different lengths. These are called***scalene**triangles.- You can do a similar lesson with quadrilaterals, using Worksheet 2. Have students identify rectangles and squares, and point out that these polygons have right angles and that rectangles have opposite sides that are congruent, while squares have all four sides congruent.

**Wrap-Up and Assessment Hints**

Students need practice identifying different polygons. Have students sort groups of polygons that are oriented differently to make sure they can identify polygons however they are turned. You can also ask students to draw different polygons using a straight edge. It is also a good idea to have children draw more than one polygon of each shape using different positions. This will allow you to get a better assessment of their true understanding of the properties of each polygon.

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