GeoGebra – Lesson 3
Using GeoGebra to draw a trapezoid
Author: Linda Fahlberg-Stojanovska
With thanks to Robert Fant
Produced with: Camtasia Studio
math247.jot.com
Key Concepts from GeoGebra
Already discussed:
,
,
,
,
Sliders
Angles with a measure
Text
Key Concepts from Mathematics for an 'inside' trapezoid
In a trapezoid, exactly one pair of opposite sides are parallel.
An 'inside' trapezoid is a parallelogram gone bad
Inside trapezoid:
Script-o-matic
1. Understand the properties of the desired trapezoid.
a.
The top and the bottom are parallel and horizontal.
b. The bottom left inside angle is <90°.
c. The bottom right inside angle is >90°.
2. Setup GeoGebra.
a.
Open GeoGebra.
b. Open the Algebra Window
i. Click View -> Algebra Window.
ii. The Algebra window will appear at left.
3. Making the base horizontal.
a.
Draw 2 points with the same y-coordinates
i.
ii.
iii.
Click on
and then click in the drawing space (bottom left) – point
A will be drawn.
Click again in the bottom right to get point B.
In the Algebra window check that A and B have the same ycoordinate. If not:
either right-click and select edit and type in the y-coordinate
or select the move tool
and click and drag B.
b. Fix the point A.
i. Right-click on A and select properties.
ii. In the properties box, select Fix object.
iii.
iv.
c.
If you want, you can make A black so users will not try to move it.
Click on Apply (or hit Enter).
Select the line tool
(not segment!)* and draw a line through A and B.
and then click on the line AB.
d. Select the point tool
i. The new point C can only move left and right along the line AB.
ii. We have fixed A and we will eventually hide B – this gives us a
horizontal base!
4. Draw a slider from 0° to 90°.
a.
*
Select the slider tool:
Best choice is the RAY tool from A through B. Then C cannot move to the left of A.
b. Click in the drawing space where you want the slider to be.
c.
In the dialog box, change the type to angle and the max to 90°.
d. Click on Apply.
(Be careful not to accidently erase the degree sign by the 90. If you do, click on
apply, then right-click on the slider and select properties and try again – without
the degree sign, GeoGebra will automatically put in 360°!)
5. Make another slider
exactly the same underneath the slider .
6. Move the sliders to positive values with
a.
Select the move tool
and
b. Click and drag the
slider to ~30°.
c.
slider to ~60°.
Click and drag the
> .
7. Make the trapezoid angles.
a.
Select the angle of given size tool
b. Click on point C and then on A. Erase 45° and then from the right arrow
select . Angle will be drawn at A and a point D.
c.
Click on point B and then on C. Erase 45° and then from the right arrow
select . Angle will be drawn at C and a point E.
d. Right-click on each of the angles
and
and de-select "Show label".
8. Draw the lines for the sides of the trapezoid.
a.
Select the line tool
.
b. Draw a line through A and D.
c.
Draw a line through C and E.
9. Find the intersection point of these two lines
a.
Select the intersection tool
.
b. Click on line AD and line CE – the point F will be drawn.
F will block the top of the trapezoid from "inverting".
10. Draw the top left vertex of the trapezoid.
a. First we want to hide the line AD.
i. Right-click on the line AD and de-select "Show object".
Note: You cannot delete this object since it is used to define other
objects. If you delete it, all of its "subobjects" are automatically
deleted. So we just hide it.
ii. Right-click on D and de-select "Show object".
b. Select the segment tool
c.
Select the point tool
and click on A and then on F.
and click on the segment A and F.
The point G can only move on the segment between A and F.
11. Draw the line for the top of the trapezoid.
a.
Select the parallel line tool
.
b. Click on G and then on the line AB.
12. Draw the top right vertex of the trapezoid.
a.
Select the intersection tool
.
b. Click on the parallel line and then on the line CE
to get the point H.
The points ACHG are the vertices of the trapezoid.
13. Hide all lines and points except A, C, H, and G.
14. Rename the points C->B, H->C, G->D.
a. Either right-click on the point and select Rename (left)
or double-click on the point, click on the Rename icon (right)
b. Type in new letter (GeoGebra automatically renames duplicates).
15. Draw the sides of the trapezoid.
a.
Select the segment tool
and click on A and then B, again on B and then
C, again on C and then D and again on D and then A.
b. Hide the labels of the segments.
c.
Select the move tool
and move the point labels to look nice.
16. Insert text – directions.
a.
Select the text tool
.
b. Click in the drawing pad where you want the text to go.
c.
Type the text you want using the arrow at right to add special symbols or
letters. We typed:
Points B and D can be moved and (hit return) angles (click on right arrow
and select) and (click on right arrow and select) can be changed using
the sliders.
d. Click on Apply.
17. Insert text – title.
a.
If not selected, select the text tool
.
b. Click in the drawing pad where you want the title to go.
c.
Type in: Trapezoid or Inside Trapezoid or whatever you want.
d. Click on Apply.
e. Right-click on the text and select "Properties".
f.
Change the font-size to 16, click on B and then click on the color patch,
select a color and then click on OK.
g. Click on Apply.
18. Select the move tool
19. Save your file!
and try out the possibilities.