# Geometer’s Sketchpad Essentials 2 – Constructing a rectangle

This is the second tutorial in the Geometer’s Sketchpad Essentials Series. In the first tutorial of this series, we used Geometer’s Sketchpad to construct medians of the triangle and found out that the medians intersect at a point. In this tutorial, we are going to learn how to use parallel and perpendicular lines to construct a rectangle.

**Step by Step Instructions**

1.) Open Geometer’s Sketchpad.

2.) Construct a segment using the **Segment** tool.

3) Select the **Text** tool and click the two points to create their labels. These points are named *A* and *B*.

4.) Next, we construct a line which is perpendicular to *AB* and passing through *A*. To do this, select the **Selection Arrow tool** and click on a blank space on the sketch pad to *deselect* all the objects.

5.) To construct the perpendicular line, select point *A* and the segment *AB, *and the click the **Construct** menu from the menu bar, and choose **Perpendicular line**.

6.) Using the same steps, construct a line perpendicular to *AB* and passing through *B*. Note: You can also create two perpendicular lines at a time by selecting the two points and the segment.

7.) To construct a point on the line passing through *A*, *deselect* all the objects by clicking the **Selection Arrow** and clicking on the blank space in the sketchpad. Select the line passing through *A*, click the **Construct** menu, and then **click Point on Perpendicular Line**.

8.) Now use the **Text** tool to label that point as *C *(Figure 2).

9.) To construct a line parallel to *AB*, deselect the line, select segment *AB* (be sure that points *A* and *B* are **not** selected), select point *C*, click the **Construct** menu from the menu bar, and select **Parallel Line**.

10.) Now, to create our fourth vertex, select the line perpendicular to *BC*, and the line through *A, *and then click **Intersection** from the **Construct** menu.

11.) Click the **Text** tool and click the fourth vertex to name it *D*.

12.) Now, we hide the lines. Select the three lines, click the **Display** menu, and click **Hide Lines**.

13.) Now, connect the three vertices using the **Segment** tool to form the rectangle. Move the vertices and observe what happens.*

Exercises:

- Reconstruct the rectangle without looking at the steps.
- Construct a rectangle triangle in another way.