Geogebra/C2/Angles-and-Triangles-Basics/English
Title of the tutorial: Angles-and-Triangles-Basics
Author: Bindu Thirumalai
Key words: Polygon, Angle and Insert Text tools, drawing pad properties, background colour, concatenate, delete, Video tutorial.
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Visual Cue |
Narration with timings |
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Show slide number 1 |
Hello Everybody. Welcome to the Geogebra tutorial Angles and Triangles Basics.
If this is the first time you are using Geogebra, please see the “Introduction to Geogebra” Tutorial on the spoken tutorial website. |
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Switch to slide number 2 (Lesson Objective ) |
To get started with Geogebra, I am using the Linux operating system Ubuntu Version 10.04 LTS and Geogebra Version 3.2.40.0
The objective of this tutorial is to verify that the sum of the interior angles of a triangle is always 180 degrees using Geogebra |
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Switch to slide number 3 (Lesson Outline) |
In this tutorial, we will learn to use the Polygon, Angle and Insert Text tool. |
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Switch to Geogebra Window |
Now First select the polygon tool. To draw a polygon, in this case a triangle, select the three vertices by clicking on the drawing pad. Then click the first vertex.
To measure the interior angles of the triangles, select the angle tool. You can measure the angle in two ways. Click clock wise the three vertices , A, B then t C, this measures the angle ABC named Alpha.
The second way is to select the line segments that form the angle. Select segment a and Segment b, this time anti-clockwise to get angle BCA named beta.
Similarly CAB, will measure the angle gamma.
Note all angles are named according to standard mathematical convention as Greek alphabets
Also if you select the vertices anti clockwise like this , C B A then the exterior angle is measured.
To add text to your drawing pad, use the insert Text Tool. Then click anywhere on the drawing pad, a text window appears
Now to display Angle ABC, type within double quotes Angle ABC = , close double quotes, add the + sign and then click on alpha. Say OK. So n I get the value of Angle ABC
Similarly to do arithmetic, to display the sum of the interior angles of this triangle, click on the insert text tool, click here on the drawing pad type in within double quotes Sum of interior angles of triangle ABC = , close double Quotes plus and open curly brackets select alpha + beta + gamma close curly brackets. Say OK. Now you see the sum displayed.
Next Select the move tool and move the free objects in this case the vertices A B or C and you will notice that the sum of the interior angles of triangle ABC is always 180 degrees.
My favourite part of this lesson is to show how when all the three vertices of the triangle are on a straight line - reduces two of the interior angles to zero and the third becomes 180 degrees like this a Straight Angle. |
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Switch to Slide 3 (Drawing Pad Properties) |
Next we will learn two more things, the drawing pad properties and how to delete an object in Geogebra |
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Geogebra Window – Drawing Pad Properties |
First the drawing pad properties. Right click anywhere on the drawing pad and then click on drawing pad
The drawing pad properties window opens. You can change the background colour of the drawing pad here.
Change properties of the axes here, both the X Axis and the Y axis here and you can change the properties of the grid here.
Some properties to note are the unit you can add for the axis and the labels you can add for the axis and the x axis to Y axis ratio.
When we are doing simple geometry we usually would like to keep it a 1:1 ratio.
When you close all changes you have made will be saved
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The Delete Option in Geogebra
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Now To delete an object on the drawing pad, move the mouse over the object, I will move the mouse over the external angle , right click you will notice that the object name appears here and then say delete, then the object is deleted.
Another way of deleting an object is to select the object on the algebra view, right click on it and say delete an object on the algebra view
Notice when I delete the angle gamma this text also disappears because it is dependent on the angle Gamma
If I want to undo what I've deleted just edit click undo or press CRTL Z
To delete multiple objects in Geogebra the easiest way to do it is to left click anywhere on the drawing pad, drag the mouse over all the objects you want to delete, undo the click, all the items are selected and then hit delete on your keyboard.
Again lets undo this by clicking undo
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Switch to Slide 4 (Writing the Text 1 ) |
Now I would like to explain the syntax of the text once again.
Text that needs to appear as-is must be within double quotes ””.As seen in the example
For values of Geogebra variables use the variable name as seen in the algebra view without quotes.
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Switch to Slide 5 (Writing the Text 2 ) |
To do arithmetic with the values use the variables within curly brackets ().
Finally to concatenate or connect text use the + sign.
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Switch to Slide 6 |
Next we will just look at some ways of matching the colours of the angles and the text
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Geogebra Window – Object Properties |
Now if I want to change the text colour I will right click and select object properties, go to colour and change the colour and say close
Now I can go to the angle here, right click , select object properties I can choose the resent window here and click on this colour for an exact match
Similarly if I want to zoom in and zoom out I use the zoom in here to zoom in and the zoom out option, click on the drawing pad to zoom out.
To change the angle unit I can go to options, angle unit and change from degrees to radians.
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Switch to Slide 6 |
So just to recap I know how to change the angle measure from radians to degrees , I can zoom in and zoom out |
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Switch to Slide 7 (Assignment) |
Now to the ASSIGNMENT.
Draw to verify - Exterior Angle of a Triangle is equal to the sum of the opposite Interior Angles
Do the following steps Draw a triangle using the polygon tool
Extend any one of the sides using the line through two points tool
Use the angle tool to measure the exterior angle and the opposite interior angles
Use the Insert Text tool to display the results Verify this by using the Move tool and moving the free objects
Verify the theorem by using the move tool and moving the free objects.
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Switch to Geogebra File Triangle Exterior Angle.ggb |
I will show you what I have done. You just need to move the move tool and move the free objects.
You will notice that the exterior angle is always equal to the sum of the opposite interior angles. |
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Switch to Slide 8 (Acknowledgement) |
I would like to acknowledge the spoken tutorial project which is part of the talk to a teacher project.
It is supported by the National Mission on Education through ICT, MHRD government of India.
You can see more information about this at this website. |
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Switch to Slide 9 |
Thank you this is Bindu signing off. Enjoy exploring Geogebra. |
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