Introduction to the Geometer’s Sketchpad

This is the first part of the Geometer’s Sketchpad Essentials Series.  In this post, we will learnabout Geometer’s Sketchpad and its environment before we use the software.

Geometer’s Sketchpad (GSP) is a commercial geometry software created my Nicolas Jackiw in the 1980s. It is similar to GeoGebra, but with fewer tools. On the one hand, it is more difficult to construct geometric objects using GSP compared to other dynamic geometry software; but, on the other hand, it can be inferred that because of the lack of tools, it may improve geometric construction knowledge better than many geometry software.

The Geometer’s Sketchpad (version 4.07) window is shown in the figure below. For now, we will be using this version in our tutorials (I have not bought a new version yet).  However, all of the tutorials in this series are also compatible with the latest version (version 5). » Read more

Wingeom Tutorial 1 – The Midline Theorem

Introduction

Wingeom is a dynamic geometry software created by Philip Exeter University.  It is capable of 2-dimensional and 3-dimensional geometric drawing and construction.

This is the first tutorial of the Wingeom Tutorial Series.  Most of the construction in this tutorial series will deal with 2-dimensions.

The Wingeom Environment

When you open Wingeom, the window shown below will appear. You have to click the Window menu, then choose the environment that you want to display.  Wingeom can construct figures in Euclidean, hyperoblic and spherical plane.

Figure 1 – The Wingeom window.

It is also capable of constructing Voronoi diagrams and tessellations.

Using Wingeom in Exploring the Midline Theorem

In this construction, we will explore the relationship of a triangle and its midline (or midsegment), the segment connecting the midpoints of its two sides as shown in Figure 2.

Figure 2 – Triangle ABC with midline DE.

In the construction below, we will construct 3 points A, B and C and connect them with the segment tool. After drawing the triangle, we will get the midpoints of AB and AC and explore the length and interior angles of the two triangles formed.

To perform the construction, follow the construction steps below and answer the questions.

Construction Steps

1.)    To open the construction window shown in Figure 2, click the Window menu and then click the 2-dim option.

2.)    Next we will show the Wingeom toolbar. The toolbar displays the tool that we can use to draw and manipulate geometric figures.  To display the toolbar, click the Btns menu and then click Toolbar.

Figure 3 – The Wingeom window and its toolbar.

3.)  The first step in our construction, we will draw the vertices of our triangle. To do this, right click three different locations on the drawing pad. Notice that Wingeom automatically names the points in alphabetical order.

4.)    Next, to construct the sides of the triangle, select the segments option button in the toolbar then drag point A to point B to construct segment AB.

5.)    Using the steps in 4, draw segments AC and BC.

6.)    Next, we will draw the midpoint of AB. To do this, click the Point menu and then click on Segment… to display the new point dialog box.

Figure 4 – The new point dialog box.

7.)    In the relative to segment, type AB, leave the coordinate to 1/2 and then click the mark button. Notice that point now lies on AB. This means that Wingeom should construct a segment halfway of AB.

8.)     To create a midpoint of AC, delete the text in the relative to segment text box and type AC. Then click the mark button.  Notice that point E now lies on AC. Click the close button in the new point dialog box to finish.

9.) Draw segment DE. Refer to step 4.

10.) Let us see what happens if we drag the vertices of the triangle. To drag the vertices of the triangle, click the drag vertices option button on the toolbar, then drag the vertices of the triangle.

11.) Now, we will display the length of DE and BC. To display the length of DE. To do this, click the Meas menu to display the measurements dialog box. Type DE in text box of the measurements dialog box and then click the ENTER key.

Figure 5 – The measurements dialog box.

12.)  Next type BC in the text box and then press the ENTER key. What can you observe about the lengths of segments BC and DE?

13.) Select the drag vertices option button on the toolbar and drag the vertices of the triangle.  Is your observation still the same?

14.) Next, we will try to observe the relationship among the interior angles of two triangles – triangle ABC and triangle ADE. First we will display the measure of angle ABC. To do this, type <ABC in the text box of the measurements dialog box and press the ENTER key.

15.) Display the measures of the following angles using step 14: ADE, AED and ACB.

16.) What do you observe about the measures of the interior angles of triangle ABC?

17.) Close the measurements dialog box and drag the vertices of the triangle (refer to step 13). Are your observations still the same?

18.) Based on your observations, make a conjecture about the relationship of triangle ABC and its midline DE.

19.) Prove your conjectures.

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.

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