GeoGebra Tutorial 3 – Constructing a Square
http://mathandmultimedia.com/2009/11/10/tutorial-3-constructing-a-square/
Problem: How will you draw an equilateral triangle without using the Regular polygon
tool?
In this tutorial, like Tutorial 2, we will mimic compass and straightedge construction
using the circle tool, the parallel line tool, the perpendicular tool to construct a square
instead of using the Regular polygon tool. We will also reinforce the use of the angle
tool, this time, learn how to use it to measure angle using three points.
Figure 1 - Square formed from radii of a circle
The idea of our construction is to construct a circle with radius AB and construct lines
parallel and perpendicular to it to form our square.
START
1.) Open the GeoGebra window. We will not need the Algebra window and
the Coordinate axes so we will hide them. To hide the Coordinate axes, click
the View menu on the menu bar, and then click Axes. To hide the Algebra window,
click View then click Algebra window.
2.) Click the Segment between two points tool and click two distinct places on the
drawing pad to construct segment AB.
3.) If the labels of the points are not displayed, click the Move button, right click
each point and click Show label from the context menu. (The context menu is the
pop-up menu that appears when you right click an object.)
4.) To construct a circle with center A passing through B, click the Circle with
Center through Point tool, click point A, then click point B. After step 4, your
drawing should look like the one shown in Figure 2.
Figure 2 - Circle with center A and passing through B
5.) To construct a line perpendicular to AB and passing through A, click the
Perpendicular line tool, click segment AB then click point A.
6.) To intersect the circle and the line, use the New Point tool and click one of the
intersections. If the label of the third point is not shown, right click the point, then
click Show label. After step 6, your drawing should look like the one shown
in Figure 3.
Figure 3 - Circle with radius AB and a line perpendicular to AB passing through A
7.) Next, we construct a line parallel to AB then passing through C. To do this, click
the inverted triangle at the bottom right of the Perpendicular line tool, then choose
the Parallel line tool. Click segment AB, then click point C.
8.) Now, we construct a line parallel to AC and passing through point B. To do this,
with the Parallel line tool still active, click line AC then click point B.
9.) Intersect the line passing through point B and point C to form point D, the fourth
vertex of the square. After step 9, your drawing should look like the one shown
in Figure 3.
Figure 3 - Square formed from radii a circle
10.) Using the Move button, move the point A or point B. What do you observe?
11.) Next we hide all the objects except the four points and segment AB. To do this,
right click each object and then uncheck Show Object from the context menu.
12.) To complete the square, connect points A and C, points C and D, and
points B and with the Segment between two points tool.
13. To verify that the quadrilateral that we created is indeed a square, right click
each side and click Object Properties.
14. In the Object Properties window, select the Basic tab. Be sure that the Show
label check box is checked and choose Value from the Show label drop down list
box. (see the last figure in Tutorial 2)
15. To measure angle A, click the Angle tool, and click the vertices in the following
order: point C, point A and then point B.
Figure 4 - Square ABCD with a reflex angle on vertex A
16. In case the angle formed is a reflex angle, right click the symbol (the green
sector), click Object Properties from the context menu.
17. In the Basic tab of the Object Properties window, uncheck the Allow Reflex
Angle check box, and then click the Close button.
18. Reveal the measure of the three other angles. Move point A or point B. What do
you observe?
19. Explain why the construction above always results to a square.