Superlesson
Project 4-1

Superlesson
Project 4-2

Superlesson
Project 4-3

Geometry

Chapter 4, Triangles

A tessellation is a repeating pattern that completely fills a plane region with congruent figures that do not overlap. Use triangle tessellations to learn about the properties of triangles.

Part A, Angles Inside the Triangle

1. Read through the explanations for creating two different types of tessellations with triangles at the Polygon tessellations Web site.

a. Make a small triangle template from cardboard. You can choose the dimensions of the triangle (but don't make it equilateral). Using this template, create two tessellations, one using each of the methods described.

b. Label the angles on your triangle template A, B, andC. Pick a point in each of your tessellations where six triangle vertices meet. Label angles that meet at the point you've chosen with A, B, or C to indicate the angle of the template with which it corresponds.

c. Use the labeled sections of each of your tessellations to find the sum of the measures of the interior angles of your triangle template. In other words, find

and explain how you know that your answer is correct.

 

Part B, Angles Outside the Triangle

2. Refer to your first tessellation. Using a different colored pen or pencil, highlight the sides of one angle of a triangle and its exterior angle. Use this section of your tessellation to find the relationship between the measure of an exterior angle of a triangle and its two remote interior angles.