PoojaMoolya at 12:02, 4 October 2019

2019-10-04T12:02:11Z

PoojaMoolya: Created page with "{|border=1 ||'''Time''' ||'''Narration''' |- || 00:01 || Welcome to this Spoken tutorial on '''Basics of Triangles''' in '''GeoGebra'''. |- ||00:06 || In this tutorial..."

2019-09-24T08:35:36Z

Created page with "{|border=1 ||'''Time''' ||'''Narration''' |- || 00:01 || Welcome to this Spoken tutorial on '''Basics of Triangles''' in '''GeoGebra'''. |- ||00:06 || In this tutorial..."

New page

{|border=1
||'''Time'''
||'''Narration'''

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|| 00:01
|| Welcome to this Spoken tutorial on '''Basics of Triangles''' in '''GeoGebra'''.

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||00:06
|| In this tutorial we will, learn to Draw a triangle and measure its angles

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||00:13
|| Display perimeter and area of the triangle

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||00:17
|| Show that sum of the angles of a triangle is 180 degrees

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||00:22
|| Show that exterior angle is equal to sum of the interior opposite angles

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||00:28
|| Also we will learn to draw,

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||00:31
|| Altitudes of the triangle and locate the orthocenter

An incircle to a triangle.

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||00:38
|| To record this tutorial, I am using; '''Ubuntu Linux''' OS version 14.04

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||00:45
|| '''GeoGebra''' version 5.0438.0-d

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||00:51
|| To follow this tutorial, learner should be familiar with '''Geogebra''' interface.

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||00:58
|| If not for relevant '''GeoGebra''' tutorials please visit our webiste.

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||01:04
|| I have opened a new '''GeoGebra '''window.

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||01:07
|| Before I begin, I will increase the '''font size''' to show the icons clearly.

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||01:13
|| Go to '''Options '''menu and select '''Font Size'''.

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||01:17
|| From the sub-menu select '''18 pt''' radio button.

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||01:22
|| For this tutorial I will uncheck the '''Axes'''.

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

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||01:29
|| And from the '''Graphics''' menu, uncheck the '''Axes'''.

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||01:33
|| Now we will draw a triangle '''ABC'''.

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||01:36
|| Click on '''Polygon''' tool.

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||01:39
|| Click on the '''Graphics view''' to draw three vertices '''A, B''' and '''C'''.

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||01:49
|| Then click on vertex '''A '''again to complete the triangle.

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||01:53
|| As we draw the triangle, observe the corresponding values in the '''Algebra view'''.

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||01:59
|| It displays: Coordinates of vertices

Lengths of the sides and Area of the triangle.

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|| 02:09
|| Now let us learn to measure the angles of the triangle.

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||02:13
|| Click on the '''Angle''' tool.

Click on the vertices '''B A C''',

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||02:23
|| '''C B A'''

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||02:29
|| '''A C B'''

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||02:35
|| Values of the angles '''alpha, beta''' and '''gamma''' are displayed in the '''Algebra view'''.

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||02:42
|| Now we will move the overlapping labels.

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||02:46
|| Click on the '''Move''' tool and drag the labels to see them clearly.

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||02:54
|| Let us display the perimeter and area of the triangle.

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||02:58
|| Click on the '''Angle''' tool drop-down and select '''Distance or Length''' tool.

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||03:05
|| Click on the triangle '''ABC'''.

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||03:08
|| Perimeter of triangle is displayed on the triangle.

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||03:12
|| Now select the '''Area''' tool and click on the triangle '''ABC''' to display it.

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||03:19
|| Next we will find the sum of the angles of the triangle '''ABC''' using '''input bar'''.

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|| 03:25
|| In the '''input bar''', open parentheses.

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||03:29
|| Inside the parentheses, select '''alpha''' from the symbols table.

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

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||03:39
|| Once again type plus sign and select '''gamma'''.

Press '''Enter'''.

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|| 03:47
|| Observe the value of angle '''delta''' in the '''Algebra view'''.

It is equal to 180 degree.

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||03:54
|| Now click on the '''Slider''' drop-down and select '''Text''' tool.

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

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||04:03
|| A text window opens on the '''Graphics view'''.

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||04:07
|| The '''Text''' tool has, An '''Edit''' box to type text

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||04:12
|| A''' Preview''' box to show the preview of the typed text

'''A Latex formula '''check box

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||04:19
|| '''Symbols '''drop-downs and

'''Objects '''drop-down.

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||04:25
|| Now we will show that, the sum of the angles of the triangle is 180 degrees.

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||04:30
|| In the '''Edit''' text box type,

'''Sum of the Angles is equal to '''

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||04:35
||Select '''alpha''' from '''Objects '''drop-down '''+''' select '''beta''' from''' Objects''' drop-down '''+''' select '''gamma''' from '''Objects''' drop-down ''' equal to '''select '''delta '''from '''Objects''' drop-down.

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||04:50
|| Observe the entered text and the values of the selected angles in the '''Preview''' box.

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||04:56
|| Click on the '''OK''' button at the bottom.

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||04:59
|| The text will be displayed on the '''Graphics view'''.

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||05:03
|| Using the '''Move '''tool drag the points '''A''', '''B''' or '''C'''.

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||05:08
|| Observe that, the sum of the angles of the triangle always shows 180 degrees.

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||05:14
|| Now we will draw a line extending segment '''BC'''.

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||05:18
|| Click on the '''Line''' tool, then click on points '''B''' and '''C'''.

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||05:24
|| Using '''Point '''tool we will mark a point '''D''' on line '''f''' next to '''C'''.

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||05:30
|| Now we will measure the exterior angle of the triangle '''ABC'''.

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||05:35
|| Click on the '''Angle''' tool and then click on the points '''DCA'''.

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|| 05:45
|| Using the '''Move''' tool, drag the overlapping labels of the angles and points.

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||05:54
|| Now, We will learn to change the colour of angle '''epsilon'''.

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||05:58
|| Right-click on angle '''epsilon'''.

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

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||06:05
|| '''Preferences''' window opens.

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||06:08
|| In the '''Color''' tab change the colour to '''Maroon''' and drag the '''Opacity''' slider.

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||06:15
|| Close the '''Preferences''' window.

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||06:18
|| Now we will check if exterior angle is equal to sum of interior opposite angles.

|-
|| 06:24
|| In the''' input bar''', open the parentheses.

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

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||06:33
|| Then press '''plus''' sign on the keyboard and select '''beta'''.

Press '''Enter'''.

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||06:41
|| Observe in the '''Algebra view''' a new angle '''tau''' equal to '''epsilon''' is created.

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||06:48
|| Angle '''tau''' is the sum of the angles '''alpha''' and '''beta'''.

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||06:53
|| Using the '''Move''' tool drag point '''C''' and observe the changes.

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

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||07:03
|| Next I will open a new window with triangle '''ABC '''and angles already drawn.

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||07:09
|| We will draw '''altitudes''' and an '''orthocentre '''to the triangle ABC.

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||07:14
|| For this first we will draw external lines on all the sides of triangle '''ABC'''.

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||07:21
|| Click the '''Line''' tool, then click on points '''A''', '''B'''.

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||07:28
|| Similarly click on points '''B''', '''C''' and '''A''', '''C'''.

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||07:35
|| Now we will draw '''altitudes''' to the triangle '''ABC.'''

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|| 07:39
|| Click on the '''Perpendicular Line''' tool.

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

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||07:46
|| Similarly click on point '''B''' and line '''h'''.

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

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||07:55
|| The three '''altitudes''' of the triangle meet at a point.

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||07:59
|| Click on the '''Intersect''' tool and mark the point of intersection as D.

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||08:06
|| Point '''D''' is the '''orthocenter''' of the triangle '''ABC'''.

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||08:10
|| Let us rename point ''' D''' as '''orthocenter'''.

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

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||08:17
|| From the sub-menu select '''Rename'''.

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||08:20
|| '''Rename''' text box opens.

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||08:23
|| In the '''Rename''' text box type '''Orthocenter'''.

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

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||08:30
|| Now press '''Ctrl+ Z''' to undo the changes.

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||08:36
|| Retain the triangle '''ABC '''with angles.

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||08:40
||Now let's construct angle bisectors to the angles.

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||08:44
|| For this, select the '''Angle Bisector''' tool from the tool bar.

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||08:49
|| Click on the points '''B''', '''A''', '''C'''.

|-
||08:56
|| '''C''', '''B''', '''A'''

|-
||09:02
||'''A''', '''C''', '''B'''.

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||09:08
|| Observe that the angle bisectors intersect at a point.

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||09:12
|| Let's mark the point as '''D''' using '''Intersect''' tool.

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||09:20
|| Let us construct a line perpendicular to segment '''BC''', passing through '''D'''.

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||09:26
|| Select the '''Perpendicular Line''' tool, click on point '''D''' and then on segment '''BC'''.

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||09:34
|| Observe that the perpendicular line intersects '''BC''' at a point.

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||09:39
|| Let's mark this point as '''E''' using '''Intersect''' tool.

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||09:45
|| Now, Let's construct a circle with centre '''D''' and which passes through '''E'''.

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||09:51
|| Click on '''Circle with Centre through point''' tool, click on point '''D''' and then click on point '''E'''.

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||10:00
|| A circle which touches all sides of the triangle is drawn.

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

|-
|| 10:10
|| Let us summarize what we have learnt.

|-
||10:13
|| In this tutorial we have learnt to, Draw a triangle and measure its angles.

|-
||10:20
|| Display perimeter and area of the triangle

|-
||10:24
|| Show that sum of the angles of a triangle is 180 degrees

|-
||10:29
|| Show that, exterior angle is equal to sum of the interior opposite angles.

|-
||10:35
|| We have also learnt to draw, Altitudes of the triangle and located the orthocenter.

|-
||10:41
|| An incircle to a triangle.

|-
||10:44
|| As an assignment, Draw a '''circumscribed circle''' to the triangle.

|-
||10:50
|| Hint: Draw perpendicular bisectors to the sides of the triangle.

|-
||10:55
|| Your assignment should look like this.

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||10:59
|| Another assignment- Draw '''medians''' to the triangle.

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||11:04
|| Mark the intersection point of''' medians'''.

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

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||11:10
|| Hint: Mark midpoints of the sides.

Join the midpoint of each side with the opposite vertex.

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||11:18
|| Your assignment should look like this.

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||11:22
|| The video at the following link summarizes the Spoken Tutorial project.

Please download and watch it.

|-
||11:30
|| The '''Spoken Tutorial Project '''team conducts workshops and gives certificates.

For more details, please write to us.

|-
||11:38
|| Please post your timed queries in this forum.

|-
||11:42
|| The Spoken Tutorial Project is funded by NMEICT, MHRD, Government of India.

More information on this mission is available at this link.

|-
|| 11:53
|| This is Madhuri Ganapathi from, IIT Bombay signing off.

Thank you for watching.
|-
|}

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 ||00:45
-|| '''GeoGebra''' version 5.0438.0-d
+|| '''GeoGebra''' version 5.0.438.0-d
 |-

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

PoojaMoolya at 12:02, 4 October 2019

PoojaMoolya: Created page with "{|border=1 ||'''Time''' ||'''Narration''' |- || 00:01 || Welcome to this Spoken tutorial on '''Basics of Triangles''' in '''GeoGebra'''. |- ||00:06 || In this tutorial..."