Chapter 6: Geogebra

Geogebra

Q.1 Fill in the blanks: (1 mark each)

1. The menu command used for hiding the axes is Axes.
2. The tool used for the measurement of an interior angle is the Angle tool.
3. Click Edità show to show and edit all the created objects.
4. Constructed objects and graphs of functions are shown in the Graphics view.
5. An angle bisector can be constructed by clicking the segment between two points tool, twice in succession.

Q.2 State whether the following statements are true or false: (1 mark each)

1. Students can learn mathematics using computer with the help of software called Geogebra. True
2. Midpoint of a segment can be found without using the ‘Midpoint or centre’ tool or the Input bar. True
3. Commands in GeoGebra can be selected from the list next to the input field on the Input bar.True
4. 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
5. With the ‘New Point’ tool selected, clicking at the intersection of two objects adds a New point at the intersection.                                                                           True
6. GeoGebra can be used to solve simultaneous equations geometrically.                  True
7. The GeoGebra screen [window] is divided into three parts.                                     True
8. By default, the GeoGebra window displays three views – Algebra, Graphics and Spreadsheet.   False
9. The command to draw a histogram is Histogram [{list of data} {list of class boundaries}].         False
10. For statistical calculations in GeoGebra, a list can be created without the Spreadsheet View.      True

Q.3 Multiple choice questions: (Single Correct Answer) (1 mark each)

1. GeoGebra was created by Markus Hohenwarter.
2. To save the construction, select file tab and click the save button
3. A file created in GeoGebra is saved with the .ggb extension.
4. A segment of fixed length is drawn using the Segment with Given Length from Point tool.
5. A histogram of a data list is drawn by typing the histogram command in the Input bar.
6. The Mode[] command in GeoGebra must be supplied with data list as parameter.
7. The Input bar is used to input data required for calculations and geometric constructions.

Q.4 Multiple choice questions: (Two Correct Answers) (2 marks each)

1. Every object in GeoGebra has algebraic and geometric representations.
2. In Geogbra, you can do different   algebraic and geometric constructions and process easily with the help of set of instructions.
3. Class boundaries specified in the Histogram[] command determines width and position of each bar of the histogram.
4. The Input bar in GeoGebra  has input field and command button.
5. Two tools in GeoGebra to draw a circle of specific radius are Circle with Centre and Radius and Compass.
6. Different complicated theorems and geometrical constructions can be understood very clearly with the help of GeoGebra.

Q.6. Answer in brief

2. Explain Graphics View and Algebra View in Geogebra.

Graphic view : Different geometric construction and graphs can be drawn in this view.

Algebra view: it shows different mathematical calculations and equations related to the graphic view.

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

5. What is the use of Geogebra in statistic?

 Statistics is an important branch of mathematics which deals with analysis of various complex surveys and calculations. Geogbra has a range of statistical uses which can be used with or without the Spreadsheet view. It has number of statistical functions and graphing tools. Eg. Mean, median, mode, Drawing a histogram etc.

Q.7.

4. What would you use to type the equation for drawing graph?

• 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.

5. Give two methods to find mean, median and mode of a given list.

Method 1: Using Input Bar:

• 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.

Method 2: Using Spreadsheet view:

• 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.

6. Give two methods in geogebra for creating a list and hence to draw the histogram.

Method 1 :  Use the input bar

Type the command histogram[{list of class boundries}, {List of raw data}]. The class boundries determines the width and position of each bar of the histogram.

Method 2: Use the spreadsheet view

• 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.

8. Practical Questions:

9. Draw a circle of radius 2.9cm using the ‘Circle with center and radius tool’. Draw a tangent to the circle at a point using the ‘tangent’ tool.

• 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.

10. Draw a circle of radius 3.1 cm. Draw tangents to the circle from a point 6.5 cm away from the center.

• 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.

  

12. Plot the points : A(4,-3) and B(-2,5), join them and find equation of the line.

• 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.

15. Verify that a segment drawn from the center of a circle to the midpoint of a 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 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.

16. Verify that the angle subtended by an arc at the center is twice the angle subtended at the circumference.

• 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.