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### Chapter 6: Geogebra

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The menu command used for hiding the axes is Axes.

The tool used for the measurement of an interior angle is the Angle tool.

Click Edità show to show and edit all the created objects.

Constructed objects and graphs of functions are shown in the Graphics view.

An angle bisector can be constructed by clicking the segment between two points tool, twice in succession.

Students can learn mathematics using computer with the help of software called Geogebra. True

Midpoint of a segment can be found without using the ‘Midpoint or centre’ tool or the Input bar. True

Commands in GeoGebra can be selected from the list next to the input field on the Input bar.True

When a segment is drawn using the ‘Segment with Given Length from Point’ tool, Moving the end-point of the segment changes the length of the segment. False

With the ‘New Point’ tool selected, clicking at the intersection of two objects adds a New point at the intersection. True

GeoGebra can be used to solve simultaneous equations geometrically. True

The GeoGebra screen [window] is divided into three parts. True

By default, the GeoGebra window displays three views – Algebra, Graphics and Spreadsheet. False

The command to draw a histogram is Histogram [{list of data} {list of class boundaries}]. False

For statistical calculations in GeoGebra, a list can be created without the Spreadsheet View. True

GeoGebra was created by Markus Hohenwarter.

To save the construction, select file tab and click the save button

A file created in GeoGebra is saved with the .ggb extension.

A segment of fixed length is drawn using the Segment with Given Length from Point tool.

A histogram of a data list is drawn by typing the histogram command in the Input bar.

The Mode[] command in GeoGebra must be supplied with data list as parameter.

The Input bar is used to input data required for calculations and geometric constructions.

Every object in GeoGebra has algebraic and geometric representations.

In Geogebra, you can do different algebraic and geometric constructions and process easily with the help of set of instructions.

Class boundaries specified in the Histogram[] command determines width and position of each bar of the histogram.

The Input bar in GeoGebra has input field and command button.

Two tools in GeoGebra to draw a circle of specific radius are Circle with Centre and Radius and Compass.

Different complicated theorems and geometrical constructions can be understood very clearly with the help of GeoGebra.

Input bar is used to create and modify algebraic coordinates and equations.

Click in the input bar.

Type the given equation in the input bar. Right click in the graphic view select the grid.

Press enter key from the keyboard. You will get the graph for the given equation.

Click in input bar and type following commands.

To calculate mean : mean[given data] . Press Enter.

To calculate median : median[given data] . Press Enter.

To calculate mode: mode[given data] . Press Enter.

Click View menu. Click on the Spreadsheet view.

Type the data on spreadsheet in column A.

Click and drag the mouse to highlight the data.

Click create list button.

Create list dialogue box will appear. Click create.

A list will appear in algebra view.

Click sum button. A button menu will appear.

Click mean to calculate mean.

Click on the view menu, select the spreadsheet view.

Type the class boundries in the first column.

Type the data in the second column.

Select the column, right click on the column and select create list for column A and B.

A list appears with a name list1, list2.

Type the command histogram{list1,list2}

Geogebra will construct the following histogram.

For the circle. Select the circle with center and radius tool.

A dialogue box appears type the radius 2.9cm and click ok. A circle appears on the screen.

Take a point on the circle using the new point tool and plot a point.

To draw a tangent select point and the circumference of the circle respectively a tangent will be constructed at the point.

Draw a segment of 6.5cm. A seg AB appears.

For the circle. Select the circle with center and radius tool from point A.

A dialogue box appears type the radius 3.1cm and click ok. A circle appears on the screen.

To draw a tangent select point B and the circumference of the circle respectively two tangents will be constructed from the point to the circle.

To plot the point: In the input bar type A=(4,-3) and B=(-2,5).

Join the points A and B using the line tool.

Geogebra will automatically generate the equation of the line and display in the algebra view.

Select the Circle with Center through Point tool. Click at a point A draw a circle at another point B. This draws a circle c with A as the center and radius AB.

Using the New Point tool, add point C on the circumference of the circle.

Select the Segment between Two points tool and draw a chord BC.

Select the midpoint or Center tool and click on the chord to get its midpoint D.

Select the segment between two points tool and draw the segment connecting A and D.

Select the Angle tool, and click on the vertices A, D and C. This shows mÐADC as α= 90.

This verifies that the segment drawn from the center of the circle to the midpoint of the chord, is perpendicular to the chord.

Select the Circle with Center through Point tool. Click at a point A draw a circle at another point B. This draws a circle c with A as the center and radius AB.

Using the New Point tool add two point C and D on the circumference of the circle.

Select the Segment between two points tool and draw the segment AB, AC, DB and DC.

Select angle tool. Click on the points BA, AC this measure the angle subtended by the arc CB, ÐBAC, as α, Similarly, click on the segments DB and DC. this measure the angle ÐBDC subtended by the arc CB at the circumference.