Difference between revisions of "GeoGebra-5.04/C2/Congruency-of-Triangles/English"
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'''Assignment''' | '''Assignment''' | ||
− | || Join the points '''D''', '''G''' and '''G''', '''E'''. | + | || Pause the video and do the following assignment on your own. |
+ | |||
+ | Join the points '''D''', '''G''' and '''G''', '''E'''. | ||
Compare the segment lengths in the '''Algebra view'''. | Compare the segment lengths in the '''Algebra view'''. |
Latest revision as of 11:45, 25 June 2020
Visual Cue | Narration |
Slide Number 1
Title slide |
Welcome to the spoken tutorial on Congruency of Triangles in GeoGebra. |
Slide Number 2
Learning Objectives |
In this tutorial we will learn to,
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Slide Number 3
System Requirement |
Here I am using,
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Slide Number 4
Pre-requisites www.spoken-tutorial.org |
To follow this tutorial, learner should be familiar with Geogebra interface.
For the prerequisite GeoGebra tutorials, please visit our website. www.spoken-tutorial.org |
Slide Number 5
Congruency of Triangles ∆ABC ≅ ∆PQR. |
First I will explain about congruency of triangles.
Two triangles are congruent if, they are of the same size and shape. All the corresponding sides and interior angles are congruent. |
Slide Number 6
SSS rule of congruency Two triangles are congruent if, three sides of one triangle are equal to the three corresponding sides of another triangle. |
We will begin with the Side Side Side rule of congruency.
This is the definition of Side Side Side rule of congruency. |
Point to the interface. | I have already opened the GeoGebra interface on my machine. |
Right-click on Graphics view >> from the sub-menu uncheck Axes check-box. | For this tutorial, I will disable the axes. |
Go to Options menu >> select Fontsize >> from the sub-menu select 18pt radio button. | I will increase the font size to 18pt for clarity. |
Click on Polygon tool >> click on Graphics view. | Now let us draw a triangle ABC.
Click on the Polygon tool and a draw a triangle ABC, as explained earlier. |
Cursor on triangle ABC. | We will construct another triangle exactly same as triangle ABC. |
Drag triangle ABC to left corner.
Click on Move tool >> drag triangle ABC. |
Using the Move tool, I will drag triangle ABC to the left side.
This will create some space, for the new construction. |
Click on the Circle with Center and Radius tool >> click on Graphics view. | Click on the Circle with Center and Radius tool, then click on the Graphics view. |
Point to the text box.
Type a in Radius text box >> click OK at the bottom. |
A Circle with Center and Radius text box opens.
In the Radius text box, type a and click on the OK button at the bottom. |
Point to the circle. | A circle with centre D and radius a is drawn. |
Click on Point tool >> click on circle. | Using the Point tool, mark a point E on the circumference of circle d. |
Click on Segment tool >> click points D and E.
Point to the Algebra view. |
Using the Segment tool join points D and E.
Note that, in the Algebra view, segment DE is same as segment BC. |
Click on Circle with Center and Radius tool >> Click on E. | Select the Circle with Center and Radius tool and click on point E. |
In the Radius text box type b >> click OK button at the bottom. | In the Radius text box, type b and click on the OK button at the bottom. |
Point to the circle. | A circle with centre E and radius b is drawn. |
Click on D.
In the Radius text box type c >> click OK button at the bottom |
Click again on point D.
In the Radius text box, type c and click on the OK button at the bottom. |
Point to the circle. | A circle with centre D and radius c is drawn. |
Point to the circles.
Point to circles g and e. |
Now we have three circles in the Graphics view.
We will mark the intersection points of the circles g and e and circles d and e. |
Click on the Intersect tool >> click on the intersection point of circles d and eas F. | Click on the Intersect tool.
Click on the intersection point of circles g and e as F. |
Click on intersection point of circles d and e as G. | Then click on the intersection point of circles d and e as G. |
Click on Segment tool >> join D, F >> join F, E. | Using the Segment tool, join the points D, F and F, E. |
Point to the circles g and e. | Here we are using the intersection point of circles g and e to get the required triangle. |
Point to the circles d and e. | If we use the intersection point of circles d and e, we will not get the required triangle. |
Slide Number 7
Assignment |
Pause the video and do the following assignment on your own.
Join the points D, G and G, E. Compare the segment lengths in the Algebra view. |
Point to the circles and triangle. | Now we will hide the circles to see the triangle DEF. |
Right-click on circle d.
Point to the sub-menu. In the sub-menu >> click on Show Object check-box. |
Right-click on circle d.
A sub-menu opens. In the sub-menu, click on Show Object check-box. |
Right-click on circle.
Point to the sub-menu. In the sub-menu >> click on Show Object check-box. |
Similarly I will hide circles e and g. |
Cursor on Graphics view. | Now we will compare the sides of the triangles ABC and DEF. |
Point to Algebra view.
Under Segment right-click on a. |
In the Algebra view, under Segment right-click on a. |
From the sub-menu opens >> select Object Properties. | From the sub-menu that opens, select Object Properties. |
Point to Preferences window. | The Preferences window opens. |
Point to a.
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Notice that a is already selected.
While holding the Ctrl key, click on b, c, f, h and i to select them. |
In Show Label drop-down >> choose Name & Value option. | In Show Label drop-down, choose Name & Value option. |
Click on x button to close. | Close the Preferences window. |
Point to the sides. | Notice that AB = DF, BC = DE and AC = EF. |
Click on Move tool >> drag points A, B or C.
Observe the drag. |
Using the Move tool, let us move the points A, B or C.
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Point to the triangles ABC and DEF. | This proves that, triangles ABC and DEF are congruent. |
Slide Number 8
ASA Rule of Congruency Two triangles are congruent if, If two angles and an included side of a triangle are equal to two corresponding angles and an included side of another triangle. |
Now we will learn to construct and prove Angle Side Angle rule of congruency.
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Click on File >> Select New Window | Let us open a new GeoGebra window.
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Click on Polygon tool >> click on Graphics view. | I will draw a triangle using the Polygon tool. |
Cursor on triangle ABC.
Click on the Angle tool and click on C B A and A C B. |
Next we will measure two angles of the triangle.
Click on the Angle tool and click on the points C B A and A C B. |
Point to the Algebra view. | The values of the angles alpha and beta are displayed in the Algebra view. |
Drag triangle ABC to a corner. | Using the Move tool, I will drag triangle ABC to the left side.
This will create some space to construct the congruent triangle. |
Click on Segment with Given Length tool >> click in Graphics view. | Click on Segment with Given Length tool and click in the Graphics view. |
Point to the text box. | Segment with Given Length text box opens. |
Type Length as a >> click OK button at the bottom. | Type Length as a and click on the OK button at the bottom. |
Point to segment DE | Segment DE is drawn. |
Point to the lengths in Algebra view. | Notice that the length of segment DE is the same as segment BC. |
Point to alpha and beta. | Now we will construct angles which are same as alpha and beta for the congruent triangle. |
Click on Angle with Given Size tool >> click on point E >> click on D. | Click on the Angle with Given Size tool, click on point E and then on point D. |
Point to the text box. | Angle with Given Size text box opens. |
Delete 45 degrees in the text box.
Select alpha from the symbols table. Click on OK button at the bottom. |
In the text box delete 45 degrees.
Select alpha from the symbols table. Click on the OK button at the bottom. |
Point to the values in Graphics view and Algebra View. | Notice that angle gamma equal to alpha is constructed at D. |
Click on point D >> point E | Next click on point D and then on point E. |
Point to the text box.
Delete 45 degrees. |
In the Angle with Given Size text box delete 45 degrees. |
Select beta from symbols table. | Select beta from the symbols table. |
Choose clockwise radio button >> click OK button. | This time choose clockwise radio button and click on OK button. |
Point to the values in Graphics view and Algebra View. | Notice that angle delta equal to beta is constructed at E. |
Point to the points E' and D' | Observe that, points E' and D' are drawn when angles gamma and delta are constructed. |
Click on Line tool >> join points D, E' and E, D'. | Using the Line tool, we will join the points D, E'(E prime) and E, D'(D prime). |
Click on Move tool to deactivate the tool.
Point to Graphics view. |
After using a particular tool, click on the Move tool to deactivate it.
This will prevent the drawing of unnecessary points in the Graphics view. |
Point to the intersection point.
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The lines g and h intersect at a point.
Using the Intersect tool, mark the point of intersection as F. |
Point to the lines h and j. | We will hide the lines g and h, as we need only the intersection point of the lines. |
Right-click on line g.
From the sub-menu, click on Show Object check-box. |
Right-click on line g and click on Show Object check-box. |
Right-click on line h.
From the sub-menu click on Show Object check-box. |
Similarly hide the line h. |
Click on Segment tool >> join points D, F >> join points F, E.
Point to the triangles ABC and DEF. |
Now using the Segment tool join D, F and F, E.
The formed triangle DEF is congruent to triangle ABC. |
Point to the values of angles and lengths in Algebra view. | In the Algebra view, compare the values of lengths and angles of the triangles. |
Point to the values. | The values indicate that the angles and side are congruent.
This proves the Angle Side Angle rule of congruency. |
Press Ctrl+A keys to select all the objects.
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Now let us delete all the objects.
Press Ctrl+A keys to select all the objects. Then press Delete key on the keyboard. |
Slide Number 9
SAS rule of Congruency Two triangles are congruent if, two sides and an included angle of a triangle are equal to corresponding two sides and an included angle of another triangle. |
Now we learn to construct and prove Side Angle Side rule of congruency.
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Click on Polygon tool >> draw a triangle ABC. | Using the Polygon tool, draw a triangle ABC. |
Point to ACB.
Click on Angle tool >>click on the points A C B'. |
Let us measure the angle A C B.
Click on the Angle tool and click on the points A C B. |
Point segment BC. | Let us draw the base of the congruent triangle. |
Click on Segment with Given Length tool >> click on Graphics view. | Click on Segment with Given Length tool and click in the Graphics view. |
Point to the text box.
Type length as a >> click OK button. Point to segment DE. |
In the Segment with Given Length text box, type length as a.
Then click on the OK button. Segment DE is drawn. |
Point to angle alpha. | Let us copy angle alpha(ACB) at point E. |
Click on Angle with Given Size tool.
Click on point D >> on point E. |
Click on the Angle with Given Size tool.
Click on point D then on point E. |
Point to the text box. | Angle Given Size text box opens. |
Delete 45 degrees in the Angle text box >> select alpha from symbols table. | In the Angle text box, delete 45 degrees and select alpha from the symbols table. |
Choose clockwise radio button >> click OK. | Choose clockwise radio button and click on the OK button. |
Point to angle beta. | Angle beta which is same as angle alpha is constructed at point E. |
Click on Line tool>>click E and D' | Using the Line tool, let us join points E, D'. |
Point to the segments b and c. | Now we need to construct two segments with lengths same as b and c. |
click on Segment with Given Length tool, click on D. | Click on the Segment with Given Length tool, and then click on point D. |
Point to the text box. | Segment with Given Length text box opens. |
Type c as length >> click OK | In the Length text box type c and click on the OK button. |
Point to segment DF. | Segment DF with length same as AB is drawn in the horizontal direction. |
Click on Circle with Centre through Point tool >> click on D >> on F. | Now click on the Circle with Centre through Point tool.
Click on point D and then click on point F. |
Point to the circle. | A circle with centre at D and passing through F, is drawn. |
Cursor on the intersection points. | Observe that circle d intersects line g at two points. |
Click on Intersect tool >> click on points of intersection. | Click on the Intersect tool and click on the points of intersection. |
Point to all the objects. | Now we will hide circle d, line g, points D' and F and segment h, to complete our drawing. |
Click the blue dots in Algebra view. | To hide, click on the blue dots corresponding to the objects in Algebra view. |
Click on Segment tool >> click on points E, G
D, G and D, H. |
Using the Segment tool , click on points D G, G, E and D, H to join them. |
Point to the triangles. | Here we see the two triangles DGE and DHE. |
Point to the triangles. | Notice from the Algebra view that triangle DGE is matching triangle ABC. |
Point to the lengths. | Now we will compare the lengths of the sides of these triangles. |
Click on Distance or Length tool, click on the segments,
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Click on the Distance or Length tool.
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Point to AB = DG,
BC=DE, AC=GE. Point to angles alpha and beta. |
Observe that AB = DG,
BC=DE, AC=GE. This indicates that all sides are congruent And angle alpha is equal to angle beta. |
Point to the triangles ABC and DGE. | The triangles ABC and DGE are congruent using SAS rule of congruency. |
Let us summarise what we have learnt. | |
Slide Number 10
Summary |
In this tutorial we have learnt to,
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Slide Number 9
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As an assignment,
Construct two triangles and prove, 1. Angle Angle Side rule of congruency 2. Hypotenuse Leg rule of congruency |
Show the assignments. | Your assignments should look as follows. |
Slide Number 11
About Spoken Tutorial project |
The video at the following link summarises the Spoken Tutorial project.
Please download and watch it. |
Slide Number 12
Spoken Tutorial workshops |
The Spoken Tutorial Project team:
conducts workshops and gives certificates For more details, please write to us. |
Slide Number 13
Forum for specific questions:
|
Please post your timed queries in this forum. |
Slide Number 14
Acknowledgement |
Spoken Tutorial Project is funded by NMEICT, MHRD, Government of India.
More information on this mission is available at this link. |
This is Madhuri Ganapathi from, IIT Bombay signing off.
Thankyou for watching. |