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

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.
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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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