## CBSE Class 9 Maths Lab Manual – Equal Division of a Line Segment

Objective
To divide a line segment into equal parts.

Prerequisite Knowledge
Intercept Theorem: If there are three (or more) parallel lines and intercepts made by them on any transversal are equal, then intercepts made by them on any other transversal are also equal.

Materials Required
A sheet of ruled paper in which all the lines are parallel and equidistant, tracing paper or transparent sheet, geometry box.

Procedure

1. Take a piece of tracing paper sheet and draw a line segment of length 10 cm or 9 cm (let line segment is to be divided into 7 equal parts). Name it as PQ.
2. Now, take a ruled sheet, and mark the lines as 0, 1, 2, 3, 4…10 from top to bottom.
3. Place the paper strip (tracing paper) on the ruled sheet such that the point P coincides as with the line (ruled sheet) marked 0, and other point Q coincides with the line marked 7 as shown in fig.(i).
4. Mark the points on PQ which are the points of intersection with lines of ruled sheet as A1, A2, A3,…A6.
5. Now remove the ruled sheet.

Observation
7 equal parts will be obtained.
PA1 = A1A2 = A2A3 = A3A4 = A4A5 = A5A6 = A6Q.
Here, marked axis PQ is a transversal on parallel lines of ruled sheet with equal intercept. Therefore, PQ also has equal intercepts (By intercept theorem).

Result
Line PQ is divided into 7 equal parts.

Learning Outcome
By paper activity, a line segment of any measurement can be divided into equal parts.

Activity Time

1. Draw a line segment of 7 cm, and divide it into 6 equal parts and draw perpendicular on the 4th point of line segment, by paper folding.
2. Take any rectangular sheet of 5 cm by 9 cm and divide the edges of sheet in 8 equal parts.
3. Take any rectangular sheet of 10 cm by 7 cm and divide along length in 10 equal parts and along the breadth in 7 equal parts (By paper folding).

Viva Voce

Question 1.
What do you mean by parallel lines ?
Two distinct lines which are not intersecting are called as parallel lines.

Question 2.
What is transversal line ?
A line intersecting two or more than two distinct lines at distinct points is called as transversal line.

Question 3.
What is intercept?
If a transversal line intersects two parallel lines, the line segment intersected between the parallel lines on the transversal is called intercept.

Question 4.
How will you state intercept theorem ?
If there are three (or more) parallel lines and the intercepts made by them on one transversal are equal, the intercepts on any other transversal are also equal.

Question 5.
What is line segment ?
Line segment is a part of a line.

Question 6.
What do you mean by fractions ?
Equal parts of a whole are called fractions.

Question 7.
What do you mean by equivalent fractions ?
Two or more fractions representing the same part of the whole are known as equivalent fractions.

Question 8.
How will you bisect a rope without measuring it ?
By folding rope and joining its end points, two equal parts of a rope will be obtained.

Question 9.
To divide a thread in 8 equal parts, how many successive folds will you give ?
7 folds.

Question 10.
Explain the trisection of a strip.
A strip is divided into three equal parts.

Question 11.
Explain the six equal divisions of a rope.
If a rope is divided into six equal parts then each part is one-sixth of rope.

Question 12.
If the intercept made by a transversal between three parallel lines is in ratio 1:2, what intercept made by another transversal?
Same ratio (1:2).

Multiple Choice Questions

Question 1.
If AB = 10 cm, is divided into 7 equal parts then what will be the value of each part ?
(i) $$\frac { 1 }{ 7 }$$ cm
(ii) $$\frac { 10 }{ 7 }$$ cm
(iii) $$\frac { 3 }{ 7 }$$ cm
(iv) none of these

Question 2.
If ratio of intercepts made by a transversal is $$\frac { 2 }{ 3 }$$ then what will be the ratio of intercepts made by another transversal ?
(i) $$\frac { 3 }{ 2 }$$
(ii) $$\frac { 2 }{ 3 }$$
(iii) $$\frac { 1 }{ 3 }$$
(iv) none of these

Question 3.
The length of a line segment is 12 cm, what is the length of each part, if it is divided into 10 equal parts ?
(i) 1.2 cm
(ii) 2.2 cm
(iii) $$\frac { 10 }{ 12 }$$ cm
(iv) none of these

Question 4.
If PQ = 9 cm, is divided into three equal parts, what is ratio of first two parts to the remaining part ?
(i) 2:1
(ii) 1:2
(iii) 3 :2
(iv) none of these

Question 5.
Which theorem is used to get the equal division of a line segment ?
(i) Pythagoras theorem
(ii) mid-point theorem
(iii) intercept theorem
(iv) none of these.

Question 6.
What do you mean by transversal line ? A line which intersects:
(i) one line
(ii) two or more lines
(iii) angle
(iv) none of these

Question 7.
Write first two equivalent fractions of $$\frac { 5 }{ 2 }$$
(i) $$\frac { 5 }{ 2 } ,\frac { 10 }{ 2 }$$
(ii) $$\frac { 10 }{ 4 } ,\frac { 15 }{ 6 }$$
(iii) $$\frac { 2 }{ 5 } ,\frac { 4 }{ 10 }$$
(iv) none of these

Question 8.
If $$\frac { 5 }{ 7 } =\frac { x }{ 35 }$$ what is the value of x?
(i) 25
(ii) 10
(iii) 1
(iv) none of these

Question 9.
Find x, if $$\frac { 21 }{ 9 } =\frac { 7 }{ x }$$
(i) 3
(ii) $$\frac { 1 }{ 3 }$$
(iii) 21
(iv) none of these

Question 10.
In the given figure, AB = BC = 4 cm, find DE, if EF = 5 cm

(i) 5 cm
(ii) 6 cm
(iii) 2 cm
(iv) none of these

1. (i)
2. (ii)
3. (i)
4. (i)
5. (iii)
6. (ii)
7. (ii)
8. (i)
9. (i)
10. (i)