# Section 10.5 Activities

## Part A: Construct an Isosceles Triangle

Use the compass tool to help you draw an isosceles triangle. Without measuring any side lengths, explain why your triangle must be isosceles. How does the compass tool work? Click on the Compass tool button. The first two clicks measure the length you want the compass to be set at. The third click determines the center of the circle.

## Question #1

Explain why your triangle must be isosceles.

## Part B: Construct an Equilateral Triangle

Follow the instructions below to construct an equilateral triangle. Step 1: Draw a circle centered at A, passing through B. Step 2: Draw a circle centered at B, passing through A. Step 3: Label one of the two points where the circles intersect C. Step 4: Connect A, B, and C with line segments.

## Question #2

Explain why this method must always produce an equilateral triangle.

## Part C: Construct a Rhombus

In the figure below, the line segments AB and AC have the same length. Use the compass tool to draw a rhombus that has AB and AC as two of its sides.

## Question #3

Describe how you constructed your rhombus.

## Part D: A Triangle with Given Lengths

The line segment AB shown below has a length of 4 units. Use the Circle With Center and Radius tool to construct a triangle that has AB as one of its sides, has a side that is 3 units long, and has another side that is 2 units long. How does the Circle With Center and Radius tool work? Click on the Circle with Center and Radius tool button. Click the point you want to be the center of your circle. Type in the desired radius length.

Describe how you constructed your triangle and why it produced a triangle with lengths 4 units, 3 units, and 2 units.