Chapter 11.3, Problem 7GP

To determine

To determine whether or not a tessellation can be created.

Answer to Problem 7GP

Yes

Explanation of Solution

Given:

Equilateral triangles

Formula used:

The measure of one interior angle $=\frac{\left(n-2\right)\times 180}{n}$

An equilateral triangle has 3 sides, $n=3.$

  $\Rightarrow$ The measure of one interior angle $=\frac{\left(3-2\right)\times 180}{3}$

  $\Rightarrow$ The measure of one interior angle $=\frac{1\times 180}{3}$

  $\Rightarrow$ The measure of one interior angle $=\frac{180}{3}$

  $\Rightarrow$ The measure of one interior angle $=60°$

Each interior angle of equilateral triangles measures $60°$ and $360°$ is evenly divisible by $60°$ .

Conclusion:

Therefore, the equilateral triangle a tessellation.