Find practice problems and solutions for these concepts at Geometry and Measurement Conversions Practice Problems.

### What's Around The Bend

- Polygons
- Classifying Triangles
- Classifying Quadrilaterals
- Perimeter
- Area
- Circles
- Pythagorean Theorem
- Volume
- Measurement Conversions

### Polygons

Plane figures are two-dimensional objects that reside on a plane. You can think of a plane like a sheet of paper that extends forever in all directions. Special figures are called **polygons**, several of which are defined here.

## Fuel for Thought
- A
polygon is a closed plane figure made up of line segments.- A
triangle is a polygon with three sides.- A
quadrilateral is a polygon with four sides.- A
pentagon is a polygon with five sides.- A
hexagon is a polygon with six sides.- An
octagon is a polygon with eight sides. |

Polygons are made up of angles and line segments called **sides**. Each angle is made up of two sides, and the point at which they meet is called the **vertex.**

### Triangles

Triangles are three-sided polygons. Triangles are classified, or grouped, in two different ways. One classification distinguishes by the sides, and another by the angles. For a triangle, you can have all three sides **congruent** (equal measure), two sides congruent, or no sides congruent.

In triangle figures, the little box drawn inside an angle stands for a right angle (90°). Here is the classification for triangles when grouped by angle:

Note that even though right triangles and obtuse triangles each have two acute angles, their classification is not affected by these angles. Acute triangles have all THREE acute angles.

### Quadrilaterals

Four-sided polygons are called **quadrilaterals**, and like triangles, there are classifications for quadrilaterals.

A quadrilateral with one pair of parallel sides (bases) is called a **trapezoid**. In an **isosceles trapezoid**, the sides that are not bases are congruent. Because the parallel bases are not the same length in a trapezoid, we call these bases *b*_{1} and *b*_{2}.

A quadrilateral with two pairs of parallel sides is called a **parallelogram**.

The two sets of opposite sides that are parallel are congruent in a parallelogram, as shown in the figure:

Parallelograms are broken down into further subgroups.

A **rectangle** is a parallelogram with four right angles.

A **rhombus** is a parallelogram with four congruent sides.

A **square** is a parallelogram with both four right angles and four congruent sides.

### Perimeter

**Perimeter** is the measure AROUND a polygon. Perimeter is an addition concept; it is a linear, one-dimensional measurement.

To find the perimeter of a polygon, add up all of the lengths of the sides of the figure. Be sure to name the units.

## Inside Track
For a square, or any rhombus, the perimeter can be found by |

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