Question

construction in exercises 17 and 18, construct an equilateral triangle whose sides are the given length.

1. 3 inches
2. 1.25 inches

Explanation:

Step1: Understand the Task

We need to construct an equilateral triangle with side length 3 inches (for problem 17). An equilateral triangle has all sides equal and all angles equal to \(60^\circ\).

Step2: Gather Tools

We will need a ruler, a compass, and a pencil.

Step3: Draw the Base

Using the ruler, draw a line segment \(AB\) of length 3 inches.

Step4: Set the Compass

Set the compass to a radius of 3 inches (the length of \(AB\)).

Step5: Draw Arcs

• Place the compass tip at point \(A\) and draw an arc above the line segment \(AB\).
• Place the compass tip at point \(B\) and draw another arc that intersects the first arc. Let the intersection point be \(C\).

Step6: Connect the Points

Using the ruler, draw line segments \(AC\) and \(BC\). Now, triangle \(ABC\) is an equilateral triangle with side length 3 inches.

Answer:

The equilateral triangle with side length 3 inches is constructed as described above. (Note: Since this is a construction problem, the final answer is the constructed triangle. If a diagram is required, follow the steps to draw it.)