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

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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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Please download and watch it.

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15:02 This is Madhuri Ganapathi from, IIT Bombay signing off.

Thank you for watching.

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