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

Time	Narration
00:01	Welcome to the spoken tutorial on Congruency of Triangles in GeoGebra.
00:07	In this tutorial we will learn to, Construct congruent triangles and Prove their congruency.
00:17	Here I am using, Ubuntu Linux OS version 14.04 GeoGebra version 5.0.438.0-d.
00:29	To follow this tutorial, learner should be familiar with Geogebra interface.
00:35	For the prerequisite GeoGebra tutorials, please visit our website.
00:40	First I will explain about congruency of triangles.
00:45	Two triangles are congruent if, they are of the same size and shape.
00:51	All the corresponding sides and interior angles are congruent.
00:56	We will begin with the Side Side Side rule of congruency.
01:02	This is the definition of Side Side Side rule of congruency.
01:08	I have already opened the GeoGebra interface on my machine.
01:13	For this tutorial, I will disable the axes.
01:17	I will increase the font size to 18pt for clarity.
01:22	Now let us draw a triangle ABC.
01:26	Click on the Polygon tool and a draw a triangle ABC, as explained earlier.
01:34	We will construct another triangle exactly same as triangle ABC.
01:40	Using the Move tool, I will drag triangle ABC to the left side.
01:46	This will create some space, for the new construction.
01:50	Click on the Circle with Center and Radius tool, then click on the Graphics view.
01:57	A Circle with Center and Radius text box opens.
02:02	In the Radius text box, type a and click on the OK button at the bottom.
02:10	A circle with centre D and radius a is drawn.
02:15	Using the Point tool, mark a point E on the circumference of circle d.
02:23	Using the Segment tool join points D and E.
02:30	Note that, in the Algebra view, segment DE is same as segment BC.
02:37	Select the Circle with Center and Radius tool and click on point E.
02:44	In the Radius text box, type b and click on the OK button at the bottom.
02:51	A circle with centre E and radius b is drawn.
02:56	Click again on point D. In the Radius text box, type c and click on the OK button at the bottom.
03:06	A circle with centre D and radius c is drawn.
03:10	Now we have three circles in the Graphics view.
03:14	We will mark the intersection points of the circles g and e and circles d and e.
03:22	Click on the Intersect tool.
03:25	Click on the intersection point of circles g and e as F.
03:31	Then click on the intersection point of circles d and e as G.
03:37	Using the Segment tool, join the points D, F and F, E.
03:46	Here we are using the intersection point of circles g and e to get the required triangle.
03:53	If we use the intersection point of circles d and e, we will not get the required triangle.
04:00	Join the points D, G and G, E.
04:04	Compare the segment lengths in the Algebra view.
04:08	Now we will hide the circles to see the triangle DEF.
04:13	Right-click on circle d. A sub-menu opens.
04:19	In the sub-menu, click on Show Object check-box.
04:24	Similarly I will hide the circles e and g.
04:30	Now we will compare the sides of the triangles ABC and DEF.
04:36	In the Algebra view, under Segment right-click on a.
04:41	From the sub-menu that opens, select Object Properties.
04:46	The Preferences window opens.
04:49	Notice that a is already selected.
04:53	While holding the Ctrl key, click on b, c, f, h and i to select them.
05:06	In Show Label drop-down, choose Name & Value option.
05:11	Close the Preferences window.
05:14	Notice that AB = DF, BC = DE and AC = EF.
05:25	Using the Move tool, let us move the points A, B or C.
05:35	Note that all the lengths change accordingly, as we drag.
05:40	This proves that, triangles ABC and DEF are congruent.
05:46	Now we will learn to construct and prove Angle Side Angle rule of congruency.
05:53	This is the definition of Angle Side Angle rule of congruency.
05:59	Let us open a new GeoGebra window.
06:03	Click on File and select New Window.
06:08	I will draw a triangle using the Polygon tool.
06:14	Next we will measure two angles of the triangle.
06:18	Click on the Angle tool and click on the points C B A and A C B.
06:35	The values of the angles alpha and beta are displayed in the Algebra view.
06:41	Using the Move tool, I will drag the triangle ABC to the left side.
06:47	This will create some space to construct the congruent triangle.
06:52	Click on Segment with Given Length tool and click in the Graphics view.
06:58	Segment with Given Length text box opens.
07:02	Type Length as a and click on the OK button at the bottom.
07:07	Segment DE is drawn.
07:10	Note that the length of segment DE is the same as segment BC.
07:16	Now we will construct angles which are same as alpha and beta for the congruent triangle.
07:23	Click on the Angle with Given Size tool, click on point E and then on point D.
07:32	Angle with Given Size text box opens.
07:36	In the text box delete 45 degrees.
07:40	Select alpha from the symbols table. Click on the OK button at the bottom.
07:47	Notice that angle gamma equal to alpha is constructed at D.
07:53	Next click on point D and then on point E.
07:59	In the Angle with Given Size text box delete 45 degrees.
08:04	Select beta from the symbols table.
08:08	This time choose clockwise radio button and click on OK button.
08:15	Notice that angle delta equal to beta is constructed at E.
08:21	Observe that, points E' and D' are drawn when angles gamma and delta are constructed.
08:29	Using the Line tool, we will join the points D, E prime and E, D prime.
08:39	After using a particular tool, click on the Move tool to deactivate it.
08:45	This will prevent the drawing of unnecessary points in the Graphics view.
08:50	The lines g and h intersect at a point.
08:54	Using the Intersect tool, mark the point of intersection as F.
09:01	We will hide the lines g and h, as we need only the intersection point of the lines.
09:08	Right-click on line g and click on Show Object check-box.
09:15	Similarly hide the line h.
09:19	Using the Segment tool join D, F and F, E.
09:26	The formed triangle DEF is congruent to triangle ABC.
09:32	In the Algebra view, compare the values of lengths and angles of the triangles.
09:40	The values indicate that the angles and side are congruent.
09:45	This proves the Angle Side Angle rule of congruency.
09:50	Now let us delete all the objects. Press Ctrl+A keys to select all the objects.
09:57	Then press Delete key on the keyboard.
10:01	Now we learn to construct and prove Side Angle Side rule of congruency.
10:07	Here is the definition of Side Angle Side rule of congruency.
10:13	Using the Polygon tool, draw a triangle ABC.
10:20	Let us measure the angle A C B. Click on the Angle tool and click on the points A C B.
10:33	Let us draw the base of the congruent triangle.
10:37	Click on Segment with Given Length tool and click in the Graphics view.
10:43	In the Segment with Given Length text box, type length as a. Then click on the OK button.
10:51	Segment DE is drawn.
10:54	Let us copy angle alpha(ACB) at point E.
10:58	Click on the Angle with Given Size tool.
11:02	Click on point D and then on point E.
11:07	Angle with Given Size text box opens.
11:11	In the Angle text box, delete 45 degrees and select alpha from the symbols table.
11:19	Choose clockwise radio button and click on the OK button.
11:25	Angle beta which is same as angle alpha is constructed at point E.
11:31	Using the Line tool, let us join points E, D' prime.
11:38	Now we need to construct two segments with lengths same as b and c.
11:45	Click on the Segment with Given Length tool, and then click on point D.
11:51	Segment with Given Length text box opens.
11:55	In the Length text box type c and click on the OK button.
12:01	Segment DF with length same as AB is drawn in the horizontal direction.
12:07	Now click on the Circle with Centre through Point tool.
12:11	Click on point D and then click on point F.
12:16	A circle with centre at D and passing through F, is drawn.
12:21	Observe that circle d intersects line g at two points.
12:26	Click on the Intersect tool and click on the points of intersection.
12:33	Now we will hide circle d, line g, points D prime and F and segment h, to complete our drawing.
12:42	To hide, click on the blue dots corresponding to the objects in the Algebra view.
12:50	Using the Segment tool , click on points D G, G, E and D, H to join them.
13:01	Here we see the two triangles DGE and DHE.
13:08	Notice from the Algebra view that triangle DGE is matching triangle ABC.
13:15	Now we will compare the lengths of the sides.
13:19	Click on the Distance or Length tool. And then click on the segments AB, BC, AC, DG, DE and GE.
13:35	Observe that AB = DG, BC=DE, AC=GE.
13:45	This indicates that all sides are congruent And angle alpha is equal to angle beta.
13:53	The triangles ABC and DGE are congruent using SAS rule of congruency.
14:01	Let us summarise what we have learnt.
14:04	In this tutorial we have learnt to, Construct congruent triangles and prove their congruency.
14:13	As an assignment, Construct two triangles and prove, 1. Angle Angle Side rule of congruency 2. Hypotenuse Leg rule of congruency
14:26	Your assignments should look as follows.
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15:02	This is Madhuri Ganapathi from, IIT Bombay signing off. Thank you for watching.

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