In this tutorial, we will use the Geometer’s Sketchpad version to mimic the compass and straightedge construction tool we use in elementary geometry.

The idea in constructing a square is to use the radii of congruent circles. Before beginning the construction, see Figure 3 so that you will have an idea of what we are going to do. In Figure 4, segment ** AB** is created, then two congruent circles, one with center

**and passing through**

*A***, the other with center**

*B***passing through point**

*B***. The intersections of the circle and the line (points C and D) are the third and the fourth vertex of the square.**

*A***Step-by-Step Constructions**

1.) Click the straightedge tool and select **Segment Tool**, then click two different locations on the drawing area.

2.) Click the **Selection Arrow Tool**, click on a blank space in the drawing pad to deselect the segment. To show the label of the two points, select the two points, click the **Display** menu, then click **Show labels**. Notice that GSP names the points alphabetically – the first ** A** and the other

**.**

*B*3.) To construct two lines perpendicular to segment ** AB**, one passing through

**and the other through**

*A***, click the segment (be sure that the two points are also selected), click the**

*B***Construct**menu, then click

**Perpendicular lines**. Your construction should look like the one shown in Figure 1.

4.) Next, we will construct a circle with center ** B** passing through

**. To do this, click the**

*A**circle tool*, click point

**and then click point**

*B***.**

*A*5.) We will now intersect the circle and the line passing through point

**. To do this, click the**

*B***Point tool**, hover over the intersection of the

**circle and the line through**

**, wait for the two objects to change their color to cyan, then click their intersection.**

*B*6.) To display the label of the third point, with the third point selected, click the

**Display**menu, then click

**Show label**.

7.) Next, create a circle with center ** A** and passing through

**. Refer to step 4.**

*B*8.) Intersect the line passing through

**and the circle with center**

*A***to construct point**

*A***.**

*D*9.) Show the label of the fourth point.

10.) Next, we will hide the circles and the lines. Click the **Selection Arrow tool**, click the two circles and the two lines, then click **Hide Path Objects**.

11.) To form the square, use the **Segment tool** to connect the vertices of the square.

12.) Move the vertices of the square and observe what happens. Explain why your observation is such.