## Learning Math: Geometry

# Polygons

## Explore the properties of polygons through puzzles and games, then proceed into a more formal classification of polygons. Look at mathematical definitions more formally, and explore how terms can have different but equivalent definitions.

### In This Session

**Part A:** Hidden Polygons

**Part B: **Classifying Polygons

**Part C: **Definitions and Proof

**Homework**

In this session, you will use puzzles and a classification game to explore polygons. You will play with the definitions of various polygons to begin to internalize their meaning. You will also begin to look at mathematical definitions more formally and explore how a term can have different, but equivalent, definitions.

For information on required and/or optional materials for this session see **Note 1** below.

### Learning Objectives

In this session, you will learn to do the following:

- Broaden your thinking about polygons
- Classify polygons according to some of their features
- Understand how to divide polygons into triangles and the implications of that
- Begin to understand mathematical definitions

### Key Terms

**New in This Session**

**Concave Polygon: **A concave polygon is any polygon with an angle measuring more than 180°. Concave polygons look like they are collapsed or have one or more angles dented in.

**Convex Polygon: **A convex polygon is any polygon that is not concave.

**Irregular Polygon: **An irregular polygon is any polygon that is not regular.

**Isosceles Trapezoid: **An isosceles trapezoid is a quadrilateral with one pair of parallel sides and congruent base angles, or it is a trapezoid with congruent base angles.

**Kite: **A kite is a quadrilateral that has two pairs of adjacent sides congruent (the same length).

**Line Symmetry/Reflection Symmetry: **A polygon has line symmetry, or reflection symmetry, if you can fold it in half along a line so that the two halves match exactly. The folding line is called the line of symmetry.

**Parallelogram: **A parallelogram is a quadrilateral that has two pairs of opposite sides that are parallel.

**Polygon: **A polygon is a two-dimensional geometric figure with these characteristics:

- It is made of straight line segments.
- Each segment touches exactly two other segments, one at each of its endpoints.
- It is closed — it divides the plane into two distinct regions, one inside and the other outside the polygon.

**Quadrilateral: **A quadrilateral is a polygon with exactly four sides.

**Rectangle: **A rectangle is a quadrilateral with four right angles.

**Regular Polygon: **A regular polygon has sides that are all the same length and angles that are all the same size.

**Rhombus: **A rhombus is a quadrilateral that has all four sides congruent.

**Square: **A square is a regular quadrilateral.

**Trapezoid: **A trapezoid is a quadrilateral that has one pair of opposite sides that are parallel.

**Venn Diagram: **A Venn diagram uses circles to represent relationships among sets of objects.

**Vertex: **A vertex is the point where two sides of a polygon meet.

### Notes

The following materials are needed:

- Loops of string (at least three loops per group or individual working alone).