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

2019-09-24T08:47:05Z

Created page with "{|border=1 ||'''Time''' ||'''Narration''' |- ||00:01 ||Welcome to this tutorial on '''Properties of Quadrilaterals '''in '''GeoGebra.''' |- ||00:07 ||In this tutorial..."

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{|border=1
||'''Time'''
||'''Narration'''

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||00:01
||Welcome to this tutorial on '''Properties of Quadrilaterals '''in '''GeoGebra.'''

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||00:07
||In this tutorial we will learn,

To construct quadrilaterals and understand the properties of quadrilaterals using '''GeoGebra'''.

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||00:19
||Here I am using:

'''Ubuntu Linux OS''', version 14.04

'''GeoGebra '''version 5.0.438.0-d

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||00:31
||To follow this tutorial, learner should be familiar with '''GeoGebra''' interface.

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|| 00:38
||If not for relevant '''GeoGebra '''tutorials, please visit our website.

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|| 00:44
||Let us begin our demonstration.

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||00:47
||I have already opened the '''GeoGebra '''interface.

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|| 00:51
||For this tutorial, I will first uncheck the '''Axes'''.

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||00:55
||To do that, right-click on '''Graphics view'''.

The '''Graphics''' menu opens.

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|| 01:01
||Click on the '''Axes''' check-box.

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||01:04
||I will increase the font size for better view.

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||01:08
||Go to '''Options''' menu, navigate to '''Font Size'''.

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|| 01:13
||From the sub-menu, select '''18 pt''' radio button.

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||01:17
||Now let us construct a parallelogram.

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||01:20
||Click on the '''Segment with Given Length''' tool.

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|| 01:24
||Click on the ''' Graphics view'''.

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||01:27
||The '''Segment with Given Length''' text box opens.

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|| 01:31
||In the '''Length field''', type 5 and click on '''OK''' button.

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|| 01:37
|| Segment '''AB''' with length 5 cm and labelled as '''f''', is drawn.

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||01:44
||Let us delete the point that was drawn mistakenly.

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|| 01:48
||This point may not be required for the actual drawing.

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||01:52
||Right-click on the point. From the sub-menu, select the '''Delete '''option.

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||01:59
||Next click on the '''Parallel Line''' tool.

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|| 02:02
||Click below line '''AB''' to draw point '''C '''then click on line '''AB'''.

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||02:09
||A parallel line to segment '''AB''' passing through '''C''', is drawn.

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||02:14
||Using '''Segment''' tool, join the points '''A''' and '''C'''.

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||02:21
||Click again on '''Parallel Line''' tool, click on segment '''AC''' and then click on point '''B'''.

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||02:31
||Two parallel lines '''g''' and '''i''' intersect at a point.

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||02:36
||Click on '''Intersect''' tool and click on the point of intersection as '''D'''.

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||02:43
||Now using the '''Segment''' tool, join the points, '''C''', '''D''' and '''D''', '''B'''.

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||02:53
||Parallelogram''' ABDC''' is now complete.

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||02:57
||We will hide the lines '''g''' and '''i''', so that we can see the parallelogram clearly.

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||03:04
||Right-click on line '''g''', from the submenu click on '''Show Object''' check-box.

Similarly I will hide the line '''i'''.

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||03:15
||Now we will explore the properties of parallelogram '''ABDC'''.

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||03:20
||From the '''Algebra view''', we can find that,

segments '''f''' and '''j''' are equal and segments '''h''' and '''k '''are equal.

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|| 03:31
||Observe that, the opposite sides are parallel and equal.

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||03:36
||Let us now measure the angles of the parallelogram.

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||03:40
||Click on '''Angle''' tool.

Click on the points '''D C A'''

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|| 03:50
|| '''C A B'''

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|| 03:55
|| '''A B D'''

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|| 04:01
|| '''B D C'''.

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||04:07
||Observe that the opposite angles are equal.

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||04:11
||Now we will convert the parallelogram '''ABDC''' to a rectangle.

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||04:16
||Click on '''Move''' tool.

Click and drag point '''C''' until you see 90 degrees angle.

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|| 04:25
|| Drag the labels to see them clearly.

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|| 04:30
||Observe that all the angles changed to 90 degrees.

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|| 04:34
||Now let us learn to construct a kite.

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||04:37
||For this I will open a new '''GeoGebra''' window.

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|| 04:41
||Click on '''File''' and select '''New Window'''.

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||04:46
||To contruct a kite, we will draw two circles that intersect at two points.

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||04:52
||Click on '''Circle with Centre through point''' tool.

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|| 04:55
||Then click on '''Graphics view.'''

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||04:58
||Point''' A''' is drawn, this is the centre of the circle.

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||05:03
||Click again at some distance from point '''A'''.

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||05:07
||Point '''B''' appears.

This completes the circle '''c'''.

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||05:13
||Similarly, we will draw another circle with centre '''C''' and passing through '''D'''.

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||05:21
||Notice that the two circles '''c''' and '''d''' intersect at two points.

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||05:26
||Click on '''Intersect''' tool and click on the circles '''c''' and '''d'''.

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||05:33
||'''E''' and '''F''' are the intersection points of the circles.

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||05:37
||Now let us draw the required quadrilateral using these circles.

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||05:42
||Click on '''Polygon''' tool.

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||05:44
||Click on the points '''A, E, C, F '''and '''A''' again to complete the quadrilateral.

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||05:57
||Notice in the '''Algebra View''' that two pairs of adjacent sides are equal.

The drawn quadrilateral is a kite.

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||06:06
||Pause the tutorial and do this assignment.

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|| 06:10
|| Measure the angles of the kite and check what happens.

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|| 06:14
|| Draw diagonals and locate the intersection point of the diagonals.

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|| 06:19
|| Measure the angle at the intersection of the diagonals.

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|| 06:23
|| Check if diagonals bisect each other.

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||06:27
||Your completed assignment should look like this.

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||06:32
||To delete all the objects, press '''Ctrl''' + '''A''' and then press '''Delete''' key on the Key board.

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||06:40
||Now let us construct a rhombus.

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||06:43
||Click on '''Segment with Given Length '''tool.

Click on the '''Graphics view.'''

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||06:49
||'''Segment with Given Length''' text box opens.

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||06:53
||In the '''Length '''field, type 4 and click on '''OK '''button.

A segment with 4 units is drawn.

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||07:03
||Let us construct a circle with center '''A''' and passing through '''B'''.

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||07:08
||Click on '''Circle with Centre through Point''' tool.

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|| 07:11
|| Click on points '''A''' and '''B''' to complete the circle.

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||07:17
||Using '''Point''' tool, mark a point '''C''' on the circumference of the circle.

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||07:23
||Click on '''Segment''' tool and then click on points '''A''' and '''C'''.

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|| 07:29
||This will join the points '''A''' and '''C.'''

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||07:32
||Click on the '''Parallel line''' tool and click on the line '''AB''' and then on point '''C'''.

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|| 07:41
||We see a line parallel to '''AB''' passing through '''C'''.

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||07:46
||Similarly, draw a parallel line to segment '''AC ''' passing through '''B'''.

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||07:53
||Notice that the lines '''i''' and '''h''' intersect at a point.

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|| 07:58
||Using '''Intersect''' tool, we will mark the point of intersection as '''D'''.

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||08:05
||Using the '''Segment''' tool, join the points '''A''', '''D''' and '''B''', '''C'''.

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||08:13
||A quadrilateral '''ABDC''' with diagonals '''AD''' and '''BC''' is drawn.

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||08:19
||The diagonals intersect at a point.

Using '''Intersect''' tool, mark the point of intersection as '''E'''.

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||08:30
||Pause the tutorial and do this assignment.

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|| 08:34
|| Check if the diagonals of the quadrilateral '''ABDC '''bisect each other.

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|| 08:40
|| Also check if the diagonals are perpendicular bisectors.

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||08:45
||Your completed assignment should look like this.

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||08:49
||Now let us construct a cyclic quadrilateral.

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|| 08:53
||For this, let us open '''Graphics 2 view'''.

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||08:57
||Go to '''View''' menu and select '''Graphics 2''' check box.

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|| 09:03
|| '''Graphics 2 view''' window opens, next to existing '''Graphics view'''.

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||09:08
||Drag the border of the existing '''Graphics view''', to see '''Graphics 2 view'''.

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||09:13
||Now select '''Regular Polygon''' tool.

Click twice on '''Graphics 2 view'''.

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||09:20
||The '''Regular Polygon''' text box opens with default value 4.

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|| 09:25
||Click on the '''OK '''button.

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||09:28
||A square '''FGHI''' is drawn in '''Graphics 2 view'''.

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||09:33
||Let's construct perpendicular bisectors to segments '''FG''' and '''GH'''.

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||09:39
||Select the '''Perpendicular Bisector''' tool from the tool bar.

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|| 09:43
||Click on the points '''F''', '''G'''and '''G''', '''H'''.

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||09:50
||Observe that the perpendicular bisectors intersect at a point.

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||09:55
||Using '''Intersect '''tool we will mark this point as '''J'''.

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||10:01
||Now, Let's construct a circle with centre as '''J''' and passing through '''F'''.

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||10:07
||Click on the '''Circle with center through Point '''tool, click on point '''J'''.

Then click on point '''F'''.

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||10:16
||A cyclic quadrilateral '''FGHI '''is drawn.

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||10:21
||Now we will display its area.

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||10:24
||From the '''Angle''' tool drop down, click on the '''Area''' tool.

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|| 10:28
||Then click on the quadrilateral '''FGHI '''to display its area.

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||10:35
||As an assignment,

Draw a trapezium

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|| 10:40
|| Measure its perimeter and area.

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||10:44
||Your completed assignment should look like this.

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|| 10:49
||Let us summarise what we have learnt.

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||10:52
||In this tutorial we have learnt, To construct quadrilaterals and understand the properties of quadrilaterals using '''GeoGebra.'''

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||11:03
||The video at the following link summarises the Spoken Tutorial project.

Please download and watch it.

|-
||11:11
||The '''Spoken Tutorial Project '''team conducts workshops using spoken tutorials and gives certificates.

For more details, please write to us.

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||11:21
||Please post your questions in this forum.

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||11:25
||Spoken Tutorial Project is funded by NMEICT, MHRD, Government of India.

More information on this mission is available at this link.

|-
|| 11:36
||This is Madhuri Ganapathi from, IIT Bombay signing off.

Thank you for watching.
|-

|}

GeoGebra-5.04/C2/Properties-of-Quadrilaterals/English-timed - Revision history

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