GeoGebra-5.04/C2/Basics-of-Triangles/English - Revision history

PoojaMoolya at 09:14, 10 October 2019

2019-10-10T09:14:59Z

Nancyvarkey at 17:41, 30 June 2018

2018-06-30T17:41:50Z

Madhurig: Created page with "{|border=1 ||'''Visual Cue''' ||'''Narration''' |- ||'''Slide Number 1 ''' '''Title slide ''' || Welcome to this Spoken tutorial on '''Basics of Triangles''' in '''GeoGebr..."

2018-06-29T11:33:46Z

Created page with "{|border=1 ||'''Visual Cue''' ||'''Narration''' |- ||'''Slide Number 1 ''' '''Title slide ''' || Welcome to this Spoken tutorial on '''Basics of Triangles''' in '''GeoGebr..."

New page

{|border=1
||'''Visual Cue'''
||'''Narration'''
|-
||'''Slide Number 1 '''

'''Title slide '''
|| Welcome to this Spoken tutorial on '''Basics of Triangles''' in '''GeoGebra'''.

|-
||'''Slide Number 2'''

'''Learning Objectives'''
|| In this tutorial we will, learn to

* Draw a triangle and measure its angles

* Display perimeter and area of the triangle

* Show that sum of the angles of a triangle is 180 degrees

* Show that exterior angle is equal to sum of the interior opposite angles

|-
||'''Slide Number 3'''

'''Learning Objectives'''
|| Also we will learn to draw,

* Altitudes of the triangle and locate the orthocenter

* An incircle to a triangle.
|-
||'''Slide Number 4'''

'''System Requirement'''
|| To record this tutorial, I am using;

Ubuntu Linux OS version 14.04

GeoGebra version 5.0438.0-d

|-
||'''Slide Number 5'''

'''Pre-requisites'''

'''www.spoken-tutorial.org'''
|| To follow this tutorial, learner should be familiar

with '''Geogebra''' interface.

If not for relevant '''GeoGebra''' tutorials please visit our webiste.

|-
||Cursor on the GeoGebra window.
|| I have opened a new '''GeoGebra '''window.

|-
||Point to the icons.
|| Before I begin, I will increase the '''font''' size to show the icons clearly.

|-
||Go to '''Options''' menu >> select '''Font Size'''.

From the sub-menu select '''18 pt''' radio button.
|| Go to '''Options '''menu and select '''Font Size'''.

From the sub-menu select '''18 pt''' radio button.

|-
||Right-click on the''' Graphics view.'''

From '''Graphics''' menu, uncheck '''Axes.'''
|| For this tutorial I will uncheck the '''Axes'''.

Right-click on the '''Graphics view.'''

And from the '''Graphics''' menu, uncheck '''Axes'''.

|-
||Cursor on the '''GeoGebra '''window.
|| Now we will draw a triangle '''ABC'''.

|-
||Click on''' Polygon''' tool>> click on Graphics view>>click on Points '''A''', '''B''', '''C''' and '''A''' again.
|| Click on '''Polygon''' tool.

Click on the '''Graphics view''' to draw three vertices '''A''', '''B''' and '''C'''.

Then click on vertex '''A '''again to complete the triangle.

|-
||Point to the values in the '''Algebra view'''.
|| As we draw the triangle, observe the corresponding values in the '''Algebra view'''.

It displays:

* Coordinates of vertices
* Lengths of the sides and
* Area of the triangle.
|-
|| Point to the triangle.
|| Now let us learn to measure the angles of the triangle.

|-
||Click on '''Angle '''tool.

Click the vertices '''BAC''', '''CBA''' , '''ACB'''.
|| Click on the '''Angle''' tool.

Click the vertices '''BAC''', '''CBA ''', '''ACB'''.

|-
||Point to the values in '''Algebra view'''.
|| Values of the angles '''alpha''', '''beta''' and '''gamma''' are displayed in the '''Algebra view'''.

|-
||Cursor on the overlapping labels.
|| Now we will move the overlapping labels.

|-
||Click on '''Move''' tool>> drag the labels.
|| Click on the '''Move''' tool and drag the labels to see them clearly.

|-
||Point to the triangle.
|| Next let us display the perimeter and area of the triangle.

|-
||Click on '''Angle '''tool drop-down >> select '''Distance or Length''' tool.
|| Click on the '''Angle''' tool drop-down and select the '''Distance or Length''' tool.
|-
||Click on the triangle '''ABC'''.

Perimeter of triangle '''ABC''' is displayed on the triangle.
|| Click on the triangle '''ABC'''.

Perimeter of triangle is displayed on the triangle.

|-
||Click on '''Angle''' tool drop-down >> select '''Area''' tool >> click on the triangle '''ABC'''.

Point to the displayed area.
|| Now select the '''Area''' tool and click on the triangle '''ABC''' to display it.

|-
||Cursor on the Triangle '''ABC'''.
|| Next we will find the sum of the angles of the triangle '''ABC''' using the '''input bar'''.

|-
|| In the '''Input bar''',

(select '''alpha+select beta+select gamma''')

Press '''Enter'''.
|| In the '''input bar''', open parentheses.

Inside the parentheses, select '''alpha''' from the symbols table.

Now type plus sign, select '''beta'''.

Once again type plus sign and select '''gamma'''.

Press '''Enter'''.

|-
|| Point to delta value in the Algebra view.
|| Observe the value of angle '''delta''' in the '''Algebra view'''.

It is equal to 180 degree.

|-
||Click on '''Text''' tool >> click on '''Graphics view'''.

Point to '''Text''' tool appears.
|| Now click on the '''Slider''' drop-down and select the '''Text''' tool.

Then click on the '''Graphics''' '''view'''.

A text window opens on the '''Graphics view'''.

|-
||Point to '''Edit''' box.

Point to '''Preview''' box.

Point to '''Latex formula''' check-box

point '''Symbols''' and '''Objects''' drop-downs.
|| The text tool has,

* An '''Edit''' box to type text

* A''' Preview''' box to show the preview of the typed text

* '''A Latex formula '''check box

* '''Symbols '''drop-downs and

* '''Objects '''drop-down.
|-
||Point to the triangle ABC.
|| Now we will show that, the sum of the angles of the triangle is 180 degrees.

|-
||Point to the Edit text box.

Type,

'''Sum of Angles = '''select '''alpha''' from '''Objects '''drop-down '''+''' select '''beta''' from''' Objects''' drop-down '''+''' select '''gamma''' from '''Objects''' drop-down '''<nowiki>= </nowiki>'''select '''delta '''from '''Objects''' drop-down.
|| In the '''Edit''' text box type,

'''Sum of the Angles <nowiki>= </nowiki>'''select '''alpha''' from '''Objects '''drop-down '''+''' select '''beta''' from''' Objects''' drop-down '''+''' select '''gamma''' from '''Objects''' drop-down '''<nowiki>= </nowiki>'''select '''delta '''from '''Objects''' drop-down.

|-
||Point to the values in the '''Preveiw '''box.
|| Observe the entered text and the values of selected angles in the '''Preview''' box.

|-
||Click on '''OK''' button.
|| Click on the '''OK''' button at the bottom.
|-
||Point to the''' Graphics view'''.
|| The text will be displayed on the '''Graphics view'''.

|-
||Click on '''Move''' tool >> drag point '''A''', '''B''' or '''C'''.
|| Using the '''Move '''tool drag the points '''A''', '''B''' or '''C'''.

Observe that, the sum of the angles of the triangle always shows 180 degrees.

|-
||Point to segment '''BC'''.

Click on '''Line''' tool >> click on points '''B''' and '''C'''.
|| Now we will draw a line extending segment '''BC'''.

Click on the '''Line''' tool, then click on points '''B''' and '''C'''.

|-
||Click on '''Point''' tool> click next to '''C'''.
|| Using the '''Point '''tool we will mark a point '''D''' on line '''f''' next to '''C'''.

|-
||Point to triangle '''ABC'''.

Click on''' Angle '''tool >> click the points '''DCA'''.
|| Now we will measure the exterior angle of triangle '''ABC'''.

Click on the '''Angle''' tool and then click on the points '''DCA'''.

|-
||Click on '''Move''' tool drag the labels of the angles and point.
|| Using the '''Move''' tool, drag the overlapping labels of the angles and points.

|-
||Point to angle '''epsilon''' in '''Graphics veiw .'''
|| We will now learn to change the colour of angle '''epsilon'''.

|-
||Right-click on angle '''epsilon'''.

From the sub-menu select '''Object Properties'''.
|| Right-click on angle '''epsilon'''.

From the sub-menu, select '''Object Properties'''.

|-
||'''Preferences''' window opens.
|| '''Preferences''' window opens.

|-
||Click on '''Color''' tab >> choose colour to '''Maroon''' >> drag '''Opacity''' slider.
|| In the '''Color''' tab change the colour to '''Maroon''' and drag the '''Opacity''' slider.

|-
||Click on '''X''' button to close.
|| Close the '''Preferences''' window.

|-
||Point to angle '''epsilon'''.
|| Now we will check if exterior angle is equal to sum of interior opposite angles.

|-
|| Point to '''input bar'''.

Open parenthesis.

Inside parenthesis,

select '''alpha''' from symbols table,

press plus sign on the keyboard,

select '''beta'''.

Press Enter.
|| In the''' input bar''', open the parentheses.

Inside the parenthesis, select '''alpha''' from the '''symbols table'''.

Then press the '''plus''' sign on the keyboard and select '''beta'''.

Press '''Enter'''.

|-
||Point to Algebra view.

Point to '''epsilon''' and '''delta'''.

Point to '''alpha''' and '''beta'''.
|| Observe - in the '''Algebra view''' a new angle '''tau''' equal to '''epsilon''' is created.

Angle '''tau''' is the sum of the angles '''alpha''' and '''beta'''.

|-
||Drag point '''C.'''

See the changes in the Algebra and Graphics views.
|| Using the '''Move''' tool drag point '''C''' and observe the changes.

We see that angle '''epsilon '''is equal to angle '''tau'''.

|-
||Click on '''Polygon''' tool to draw triangle ABC.

Click on '''Angle''' tool to measure the angles('''BAC''', '''CBA''', '''ACB''')
|| Next I will open a new window with triangle '''ABC '''and angles already drawn.

|-
||Cursor on triangle '''ABC'''.
|| Then we will draw '''altitudes''' and an '''orthocentre '''to the triangle ABC.

|-
||Point to the sides of the traingle.
|| For this we will first draw external lines on all the sides of triangle '''ABC'''.

|-
||Click on '''Line''' tool >> click on points '''A''', '''B'''.
|| Click the '''Line''' tool then click on points '''A''', '''B'''.

|-
||click on points '''B''', '''C''' and '''A''', '''C'''.
|| Similarly click on points '''B''', '''C''' and '''A''', '''C'''.
|-
||Point to the triangle.
|| Now we will draw '''altitudes''' to the triangle '''ABC.'''

|-
||Click on '''Perpendicular line''' tool.

Click on point '''A''' and line '''g'''
|| Click on the '''Perpendicular Line''' tool.

Click on point '''A''' and line '''g'''.

|-
||click on point '''B''' and line '''h'''.

Click on point '''C''' and line '''f'''.
|| Similarly click on point '''B''' and line '''h'''.

Click on point '''C''' and line '''f'''.

|-
||Point to the intersection.
|| The three '''altitudes''' of the triangle meet at a point.

|-
||Click on '''intersect''' >> mark the point of intersection as '''D'''.

Point to '''D'''.
|| Click on the '''Intersect''' tool and mark the point of intersection as D.

Point '''D''' is the '''orthocenter''' of the triangle '''ABC'''.

|-
||Right-click on point '''D'''.

From the sub-menu select '''Rename'''.
|| Let us rename point ''' D''' as '''orthocenter'''.

Right-click on point '''D'''.

From the sub-menu select '''Rename'''.

|-
||Point to '''Rename''' text box.

Type '''Orthocenter.'''

Click on '''OK''' button at the bottom.
|| '''Rename''' text box opens.

In the '''Rename''' text box type '''Orthocenter'''.

Click on the '''OK''' button at the bottom.

|-
||press '''Ctrl+ Z''' to undo the process.

Point to the triangle '''ABC'''.
|| Now press '''Ctrl+ Z''' to undo the changes.

Retain the triangle '''ABC '''with its angles.

|-
||Point to the angles.
|| Let's now construct angle bisectors to the angles.

|-
||Select '''Angle Bisector''' tool >> click point '''B, A, C'''.

Click on points '''C,B, A''' >> click on points '''A''', '''C''', '''B'''.
|| For this, select the '''Angle Bisector''' tool from the tool bar.

Click on the points '''B''', '''A''', '''C'''.

'''C''', '''B''', '''A''' and '''A''', '''C''', '''B'''.

|-
||Hover the mouse on point of intersection

Click on ''' Intersect''' tool >> click point of intersection.
|| Observe that the angle bisectors intersect at a point.

Let's mark this point as '''D''' using '''Intersect''' tool.

|-
||Point to segment '''BC'''.

Click '''Perpendicular Line''' tool >> click on point '''D''' >> click on segment '''BC'''.
|| Let's construct a line perpendicular to segment '''BC''', passing through '''D'''.

Select the '''Perpendicular Line''' tool, click on point '''D''' and then on segment '''BC'''.

|-
||Point to the point of intersection.

Click on '''Intersect''' tool >> click point of intersection.
|| Observe that the perpendicular line intersects '''BC''' at a point.

Let's mark this point as '''E''' using '''Intersect''' tool.

|-
||Click on '''Circle with Centre through point '''tool >> click on point '''D''' >> click on point '''E'''.

Point to the '''incircle'''.
|| Let's now construct a circle with centre as '''D''' and which passes through '''E'''.

Click on '''Circle with Centre through point''' tool, click on point '''D''' and then point '''E'''.

A circle which touches all sides of the triangle is drawn.

This circle is the '''incircle '''to the triangle ABC.

|-
||
|| Let us summarize what we have learnt.

|-
||'''Slide Number 6'''

'''Summary'''
|| In this tutorial we have learnt to,

* Draw a triangle and measure its angles.

* Measure area and perimeter of the triangle

* Show that, the sum of the angles of a triangle is 180 degrees

* Show that, exterior angle is equal to sum of the interior opposite angles.

|-
||'''Slide Number 7'''

'''Summary'''
|| We have also learnt to draw,

* Altitudes of the triangle and located the orthocenter.

* incircle to a triangle.
|-
||'''Slide Number 8'''

'''Assignment 1'''
|| As an assignment,

Draw a '''circumscribed circle''' to the triangle.

Hint: Draw perpendicular bisectors to the sides of the triangle.

|-
||Show the Assignment.
|| Your assignment should look like this

|-
||'''Slide Number 9'''

'''Assignment 2'''
|| Another assignment-

Draw '''medians''' to the triangle.

Mark the intersection point of''' medians'''

Rename the point as '''centroid.'''

Hint: Mark midpoints of the sides

Join the midpoint of each side with the opposite vertex.

|-
||Show the Assignment.
|| Your assignment should look like this.

|-
||'''Slide Number 10'''

'''About Spoken Tutorial project'''
|| The video at the following link summarizes the Spoken Tutorial project.

Please download and watch it.

|-
||'''Slide Number 11'''

'''Spoken Tutorial workshops'''
|| The '''Spoken Tutorial Project '''team:

conducts workshops and

* gives certificates.

For more details, please write to us.

|-
||'''Slide Number 12'''

'''Forum for specific questions:'''

Do you have questions in THIS '''Spoken Tutorial'''?

* Please visit this site

* Choose the minute and second where you have the question.

* Explain your question briefly

* Someone from our team will answer them.

|| Please post your timed queries in this forum.

|-
||'''Slide Number 13'''

'''Acknowledgement'''
|| Spoken Tutorial Project is funded by NMEICT, MHRD, Government of India.

More information on this mission is available at this link.

|-
||
|| This is Madhuri Ganapathi from, IIT Bombay signing off.

Thank you for watching.
|-
|}

@@ Line 39: / Line 39: @@
 *'''Ubuntu Linux''' OS version 14.04
-*'''GeoGebra''' version 5.0438.0-d
+*'''GeoGebra''' version 5.0.438.0-d
 |-

@@ Line 37: / Line 37: @@
 || To record this tutorial, I am using;
-Ubuntu Linux OS version 14.04
+*'''Ubuntu Linux''' OS version 14.04
-GeoGebra version 5.0438.0-d
+*'''GeoGebra''' version 5.0438.0-d
 |-
@@ Line 61: / Line 61: @@
 |-
 ||Point to the icons.
-|| Before I begin, I will increase the '''font''' size to show the icons clearly.
+|| Before I begin, I will increase the '''font size''' to show the icons clearly.
 |-
@@ Line 81: / Line 81: @@
 Right-click on the '''Graphics view.'''
-And from the '''Graphics''' menu, uncheck '''Axes'''.
+And from the '''Graphics''' menu, uncheck the '''Axes'''.
 |-
@@ Line 91: / Line 91: @@
 || Click on '''Polygon''' tool.
-Click on the '''Graphics view''' to draw three vertices '''A''', '''B''' and '''C'''.
+Click on the '''Graphics view''' to draw three vertices '''A, B''' and '''C'''.
@@ Line 105: / Line 105: @@
 * Lengths of the sides and
 * Area of the triangle.
 |-
 || Point to the triangle.
@@ Line 116: / Line 117: @@
-Click the vertices '''BAC''', '''CBA ''', '''ACB'''.
+Click the vertices '''B A C, C B A, A C B'''.
 |-
 ||Point to the values in '''Algebra view'''.
-|| Values of the angles '''alpha''', '''beta''' and '''gamma''' are displayed in the '''Algebra view'''.
+|| Values of the angles '''alpha, beta''' and '''gamma''' are displayed in the '''Algebra view'''.
 |-
@@ Line 132: / Line 133: @@
 |-
 ||Point to the triangle.
-|| Next let us display the perimeter and area of the triangle.
+|| Let us display the perimeter and area of the triangle.
 |-
@@ Line 199: / Line 200: @@
 point '''Symbols''' and '''Objects''' drop-downs.
-|| The text tool has,
+|| The '''Text''' tool has,
 * An '''Edit''' box to type text
@@ Line 219: / Line 220: @@
 Type,
-'''Sum of Angles = '''select '''alpha''' from '''Objects '''drop-down '''+''' select '''beta''' from''' Objects''' drop-down '''+''' select '''gamma''' from '''Objects''' drop-down '''<nowiki>= </nowiki>'''select '''delta '''from '''Objects''' drop-down.
+'''Sum of Angles = '''
 || In the '''Edit''' text box type,
-'''Sum of the Angles <nowiki>= </nowiki>'''select '''alpha''' from '''Objects '''drop-down '''+''' select '''beta''' from''' Objects''' drop-down '''+''' select '''gamma''' from '''Objects''' drop-down '''<nowiki>= </nowiki>'''select '''delta '''from '''Objects''' drop-down.
+'''Sum of the Angles <nowiki>= </nowiki>'''
 |-
 ||Point to the values in the '''Preveiw '''box.
-|| Observe the entered text and the values of selected angles in the '''Preview''' box.
+|| Observe the entered text and the values of the selected angles in the '''Preview''' box.
 |-
@@ Line 261: / Line 266: @@
 Click on''' Angle '''tool >> click the points '''DCA'''.
-|| Now we will measure the exterior angle of triangle '''ABC'''.
+|| Now we will measure the exterior angle of the triangle '''ABC'''.
@@ Line 303: / Line 308: @@
 Open parenthesis.
-Inside parenthesis,
+Inside parentheses, select '''alpha''' from symbols table.
-select '''alpha''' from symbols table,
+Press plus sign on the keyboard,
-−
-press plus sign on the keyboard,
 select '''beta'''.
@@ Line 315: / Line 318: @@
-Inside the parenthesis, select '''alpha''' from the '''symbols table'''.
+Inside the parentheses, select '''alpha''' from the '''symbols table'''.
@@ Line 497: / Line 500: @@
 * Draw a triangle and measure its angles.
-* Measure area and perimeter of the triangle
+* Display perimeter and area of the triangle
-* Show that, the sum of the angles of a triangle is 180 degrees
+* Show that sum of the angles of a triangle is 180 degrees
 * Show that, exterior angle is equal to sum of the interior opposite angles.
@@ Line 511: / Line 514: @@
 * Altitudes of the triangle and located the orthocenter.
-* incircle to a triangle.
+* An incircle to a triangle.
 |-
 ||'''Slide Number 8'''
@@ Line 519: / Line 522: @@
-Draw a '''circumscribed circle''' to the triangle.
+*Draw a '''circumscribed circle''' to the triangle.
+*Hint: Draw perpendicular bisectors to the sides of the triangle.
 Hint: Draw perpendicular bisectors to the sides of the triangle.
 |-
 ||Show the Assignment.
-|| Your assignment should look like this
+|| Your assignment should look like this.
 |-
@@ Line 535: / Line 537: @@
-Draw '''medians''' to the triangle.
+*Draw '''medians''' to the triangle.
-Mark the intersection point of''' medians'''
+*Mark the intersection point of''' medians'''.
-Rename the point as '''centroid.'''
+*Rename the point as '''centroid.'''
-Hint: Mark midpoints of the sides
+*Join the midpoint of each side with the opposite vertex.
-−
 Join the midpoint of each side with the opposite vertex.
 |-
@@ Line 562: / Line 563: @@
 '''Spoken Tutorial workshops'''
-|| The '''Spoken Tutorial Project '''team:
+|| The '''Spoken Tutorial Project '''team conducts workshops and gives certificates.
-−
 conducts workshops and
-−
-* gives certificates.
 For more details, please write to us.