Question-Answers of Chapter 6 (GeoGebra)

Q1. Match the following .

1.--- b

2.—d

3.—e

4.—a

5.—c

Q2. Fill in the blanks

.

1. Tools used for measurementof interior angle is Angle Tool.

2. Edit show and edit all the created objects.

3. Construction of objects and graphs of functions is shown by Graphics View .

4. Tools used for hiding the axes is Axes tool.

5. Angle bisector of an angle can be constructed using Segment between Two Points tool by clicking two times in succession

Q3. Give uses of following tool.

1. To construct tangents

2. To draw line segment

3. To construct a perpendicular bisector

4. To construct a perpendicular line

5. To construct a parallel line

Q4. Answer the following.

1. Give names of different parts of the GeoGebra screen.

Ans. The different parts of the GeoGebra window are (i) Title bar , (ii) Menu bar , (iii) Tool bar , (iv) Algebra View , (v) Graphic View and (vi) Input bar

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

Ans. Input bar, Keyboard and the dropdown menus (Next to the Input bar) are used for typing the equation for drawing a graph.

3. Give two methods to find mean, mode and median of given data.

Ans. The two methods to find mean, median and mode are using the (i) Input bar and by using the (ii) Input bar & Spreadsheet view.

1] Method I :- Using Input bar – Type the sample data in the Input bar. For eg. Mean[15,20,30,40,50]

The Algebra view displays the values.

2] Method II :- Using the spreadsheet and Input bar - Enable the spreadsheet using view menu. Enter the data in the column or row. Select all the data by dragging the mouse and create list from the right click menu. After that we can give the command in the input bar using the list menu. For eg. L1 is the list name with sample data. In the Input bar, write Mean[L1] . The Algebraic view displays the value.

4. Short note on GeoGebra

Ans. Geogebra is a free, open source and multiplatform software software that combines dynamic geometry , algebra, calculus, spreadsheet, graphing and statistics is one easy – to use package. The name , GeoGebra is derived from Geometry and Algebra.

GeoGebra was created by Markus Hohenwarter in 2001-02 as part of his Masters and PhD project in Mathematics. It was specially designed for middle school and high school students and has won several prestigious awards.

GeoGebra is multi-faceted tool. It can be used as both teaching & a learning tool.

Parts of the GeoGebra windows are

(1) Title bar – displays the program name and the name of the document.

(2) Menu bar – it is situated in the top part of the geogebra window containing menus like File, Edit, View etc..

(3) Tool bar – it is located under the menu bar. The tool bar is divided into tool boxes each containing one or more tool.

(4) Algebra View – shows the different mathematical calculations and equations related in the Graphic view.

(5) Graphics View – shows the different geometric construction and graph.

(6) Input bar – it is used to input data required for calculation and geometric construction.

The software can be used to explore and discover mathematical properties and as a tool for the creation of interactive teaching material. The object so constructed can be manipulated and explored either interactively in the graphics view or by changing the parameter of the Agebra view, making the subject more interesting and effective. A file created in GeoGebra is saved with .ggb extension.

Q 5. Solve the following examples using GeoGebra.

5. Construct an equilateral triangle PQR and measure its angles.

Ans. Steps for Solution :

(1) First we have to select view menu in that we have to click on axes option for getting clear screen.

(2) For construction of an equilateral triangle, select ‘regular polygon’ tool .

(3) Create an equilateral triangle by selecting two base points. Then a window will open to specify the number of sides, then type 3 and click on ‘OK’

(4) To measure the angle , click on angle tool from the construction tool and select the points in counter clockwise.

6. Construct a regular polygon with 6 side . Use ‘polygon’ tool.

Ans. Steps for Solution :

(1) First we have to select view menu in that we have to click on axes option for getting clear screen.

(2) For construction of an regular polygon, select ‘regular polygon’ tool .

(3) Select two base points A and B.

(4) Type the number of sides of the polygon (Enter ‘6’)

8. Draw angle with measurement 133o and bisect it with ‘angle bisector’ tool.

Ans. Steps for Solution :

(1) First we have to select view menu in that we have to click on axes option for getting clear screen.

(2) Select the ‘angle with given size’ . option and select two points on the graphic section and enter the measurement of the angle (133o)

(3) Then the third point will be displayed. Then select segment between two points and select the points in the order.

(4) Select the angle bisector and select the points in the order (A,B,A’).

10. Draw a circle with radius 3.1 cm and draw tangents to the circle from points 6.5 cm away from centre.

Ans. Steps for Solution :

(2) For drawing circle with given radius we have taken ‘circle with centre and radius ‘ tool.

(3) We have inputed given radius 3.1 cm in input window which was displayed on screen and click on ‘OK’ option for getting circle.

(4) Select ‘segment with fixed length ‘ option from the tool and click on the centre of the circle. Then the input box will appear to enter the length, type 6.5 in the input box, a line will be drawn by joining the centres and the point B which is 6.5 cm away from the centre.

(5) For construction of tangent , select ‘tangent tool’ after that click on the point B which is 6.5 cm away from the centre and on circumference of circle respectively. Tangent will be constructed at that point.

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

Ans. Steps for Solution :

(1) Here we want axes for establishing given points . For that we have selected ‘Axes’ and ‘Grid’ tool view menu.

(2) We have taken ‘New Point’ tool for plotting given points.

(3) For drawing line, click on ‘line through two points’ tool.

(4) Now the Algebra view shows the equation 4x+3y=7