Chapter 4.1, Problem 53PPS

To determine

Toexplain:

The construction of equilateral triangle and draw the triangle.

Answer to Problem 53PPS

  $△ABC$ Is an equilateral triangle is explained below.

Explanation of Solution

First draw a line $p$ . Select a point on $p$ , and label it as $A$ .

  

Draw a circle centered at $A$ . Label as $B$ the intersection point on the right.

  

Draw another circle centered at $B$ with the same radius with the previous circle. Label as $C$ the intersection point above $p$ . Draw $\overline{AC}$ and $\overline{BC}$ . Then, $△ABC$ is an equilateral triangle.

  

Use a ruler to measure three sides of $△ABC$ . One obtains,

  $AB=2.54cm,BC=2.54cm,AC=2.54cm$

So, $△ABC$ is an equilateral triangle, because three side lengths are the same.

In the construction side of $△ABC$ are the radii of the two congruent circles. So, $△ABC$ is an equilateral triangle