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

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Time Narration
00:01 Welcome to this Spoken tutorial on Basics of Triangles in GeoGebra.
00:06 In this tutorial we will, learn to Draw a triangle and measure its angles
00:13 Display perimeter and area of the triangle
00:17 Show that sum of the angles of a triangle is 180 degrees
00:22 Show that exterior angle is equal to sum of the interior opposite angles
00:28 Also we will learn to draw,
00:31 Altitudes of the triangle and locate the orthocenter

An incircle to a triangle.

00:38 To record this tutorial, I am using; Ubuntu Linux OS version 14.04
00:45 GeoGebra version 5.0438.0-d
00:51 To follow this tutorial, learner should be familiar with Geogebra interface.
00:58 If not for relevant GeoGebra tutorials please visit our webiste.
01:04 I have opened a new GeoGebra window.
01:07 Before I begin, I will increase the font size to show the icons clearly.
01:13 Go to Options menu and select Font Size.
01:17 From the sub-menu select 18 pt radio button.
01:22 For this tutorial I will uncheck the Axes.

Right-click on the Graphics view.

01:29 And from the Graphics menu, uncheck the Axes.
01:33 Now we will draw a triangle ABC.
01:36 Click on Polygon tool.
01:39 Click on the Graphics view to draw three vertices A, B and C.
01:49 Then click on vertex A again to complete the triangle.
01:53 As we draw the triangle, observe the corresponding values in the Algebra view.
01:59 It displays: Coordinates of vertices

Lengths of the sides and Area of the triangle.

02:09 Now let us learn to measure the angles of the triangle.
02:13 Click on the Angle tool.

Click on the vertices B A C,

02:23 C B A
02:29 A C B
02:35 Values of the angles alpha, beta and gamma are displayed in the Algebra view.
02:42 Now we will move the overlapping labels.
02:46 Click on the Move tool and drag the labels to see them clearly.
02:54 Let us display the perimeter and area of the triangle.
02:58 Click on the Angle tool drop-down and select Distance or Length tool.
03:05 Click on the triangle ABC.
03:08 Perimeter of triangle is displayed on the triangle.
03:12 Now select the Area tool and click on the triangle ABC to display it.
03:19 Next we will find the sum of the angles of the triangle ABC using input bar.
03:25 In the input bar, open parentheses.
03:29 Inside the parentheses, select alpha from the symbols table.

Now type plus sign, select beta.

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

Press Enter.

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

It is equal to 180 degree.

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

Then click on the Graphics view.

04:03 A text window opens on the Graphics view.
04:07 The Text tool has, An Edit box to type text
04:12 A Preview box to show the preview of the typed text

A Latex formula check box

04:19 Symbols drop-downs and

Objects drop-down.

04:25 Now we will show that, the sum of the angles of the triangle is 180 degrees.
04:30 In the Edit text box type,

Sum of the Angles is equal to

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.
04:50 Observe the entered text and the values of the selected angles in the Preview box.
04:56 Click on the OK button at the bottom.
04:59 The text will be displayed on the Graphics view.
05:03 Using the Move tool drag the points A, B or C.
05:08 Observe that, the sum of the angles of the triangle always shows 180 degrees.
05:14 Now we will draw a line extending segment BC.
05:18 Click on the Line tool, then click on points B and C.
05:24 Using Point tool we will mark a point D on line f next to C.
05:30 Now we will measure the exterior angle of the triangle ABC.
05:35 Click on the Angle tool and then click on the points DCA.
05:45 Using the Move tool, drag the overlapping labels of the angles and points.
05:54 Now, We will learn to change the colour of angle epsilon.
05:58 Right-click on angle epsilon.

From the sub-menu, select Object Properties.

06:05 Preferences window opens.
06:08 In the Color tab change the colour to Maroon and drag the Opacity slider.
06:15 Close the Preferences window.
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.

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

Press Enter.

06:41 Observe in the Algebra view a new angle tau equal to epsilon is created.
06:48 Angle tau is the sum of the angles alpha and beta.
06:53 Using the Move tool drag point C and observe the changes.

We see that angle epsilon is equal to angle tau.

07:03 Next I will open a new window with triangle ABC and angles already drawn.
07:09 We will draw altitudes and an orthocentre to the triangle ABC.
07:14 For this first we will draw external lines on all the sides of triangle ABC.
07:21 Click the Line tool, then click on points A, B.
07:28 Similarly click on points B, C and A, C.
07:35 Now we will draw altitudes to the triangle ABC.
07:39 Click on the Perpendicular Line tool.

Click on point A and line g.

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

Click on point C and line f.

07:55 The three altitudes of the triangle meet at a point.
07:59 Click on the Intersect tool and mark the point of intersection as D.
08:06 Point D is the orthocenter of the triangle ABC.
08:10 Let us rename point D as orthocenter.

Right-click on point D.

08:17 From the sub-menu select Rename.
08:20 Rename text box opens.
08:23 In the Rename text box type Orthocenter.

Click on the OK button at the bottom.

08:30 Now press Ctrl+ Z to undo the changes.
08:36 Retain the triangle ABC with angles.
08:40 Now let's construct angle bisectors to the angles.
08:44 For this, select the Angle Bisector tool from the tool bar.
08:49 Click on the points B, A, C.
08:56 C, B, A
09:02 A, C, B.
09:08 Observe that the angle bisectors intersect at a point.
09:12 Let's mark the point as D using Intersect tool.
09:20 Let us construct a line perpendicular to segment BC, passing through D.
09:26 Select the Perpendicular Line tool, click on point D and then on segment BC.
09:34 Observe that the perpendicular line intersects BC at a point.
09:39 Let's mark this point as E using Intersect tool.
09:45 Now, Let's construct a circle with centre D and which passes through E.
09:51 Click on Circle with Centre through point tool, click on point D and then click on point E.
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.
10:59 Another assignment- Draw medians to the triangle.
11:04 Mark the intersection point of medians.

Rename the point as centroid.

11:10 Hint: Mark midpoints of the sides.

Join the midpoint of each side with the opposite vertex.

11:18 Your assignment should look like this.
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.

Contributors and Content Editors

PoojaMoolya