PoojaMoolya: Created page with "{|border=1 ||'''Time''' ||'''Narration''' |- || 00:01 || Welcome to the spoken tutorial on '''Congruency of Triangles''' in '''GeoGebra'''. |- || 00:07 || In this tuto..."

2019-09-24T08:45:28Z

Created page with "{|border=1 ||'''Time''' ||'''Narration''' |- || 00:01 || Welcome to the spoken tutorial on '''Congruency of Triangles''' in '''GeoGebra'''. |- || 00:07 || In this tuto..."

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{|border=1
||'''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.

|-
|| 14:31
|| The video at the following link summarises the Spoken Tutorial project.

Please download and watch it.

|-
||14:39
|| The '''Spoken Tutorial Project '''team: conducts workshops and gives certificates

For more details, please write to us.

|-
||14:47
|| Please post your timed queries in this forum.

|-
|| 14:51
|| Spoken Tutorial Project is funded by NMEICT, MHRD, Government of India.

More information on this mission is available at this link.

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

Thank you for watching.
|-
|}

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

PoojaMoolya: Created page with "{|border=1 ||'''Time''' ||'''Narration''' |- || 00:01 || Welcome to the spoken tutorial on '''Congruency of Triangles''' in '''GeoGebra'''. |- || 00:07 || In this tuto..."