## CaR Tutorial 2 – The MidSegment Theorem

In the previous CaR tutorial, we constructed and isosceles triangle. In this tutorial we are going to explore the properties of the segment connecting the midpoints of its two sides. In this tutorial we are going to learn the following:

• use the move tool, triangle tool and segment tool
• find the midpoint of two a segment
• measure angles using the angle tool
• edit properties and reveal measures of angles and segments

Construction Steps

## CaR Tutorial 1- Constructing an Isosceles Triangle

CaR or Compass and Ruler is a free dynamic geometry software written in Java by Rene Grothman. The CaR window is shown below.

Figure 1 - The Compass and Ruler window.

The upper part of the window contains the menu bar and toolbar. The toolbar contain tools in constructing and editing mathematical objects. The left window below the toolbar is the Objects window and the right pane is the Drawing pad where we construct drawings.

Tutorial 1 – Constructing an Isosceles Triangle

In the first tutorial, we are going to create an isosceles triangle by using the center of the circle and two points on its circumference.

 1.) We will not need the Coordinate axes so click the Show grid icon until the Show the Grid icon until the grid or axes is not shown. 2.)Click the Circle tool, then click the drawing pad to determine the center of the circle, and click another location to determine its radius. 3.) Click the Point tool and click another location on the circumference circle. After step 3, your drawing should look like the figure below. Figure 2 - Circle with 2 points on its circumference. 4.) Click the Segment tool and two points to construct a side of the triangle. Continue until the triangle is formed. 5.) Click the Move button to drag the points and observe what happens to the triangle. Explain why the triangle is always isosceles. 6.) Click the Hide object button and click the circle to hide it. 7.) Next, we will change the name of the points and display their names. To do this, right click a point to display the Edit Point dialog box. In the Name text box, type A, then click the Show Object Names icon. Figure 1 - The Edit Point Dialog box. Use the same process to change the name of the other points.

Congratulations, you have finished the first Compass and Ruler tutorial.