**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**

- 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.

- Now, take a ruled sheet, and mark the lines as 0, 1, 2, 3, 4…10 from top to bottom.
- 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).
- Mark the points on PQ which are the points of intersection with lines of ruled sheet as A
_{1}, A_{2}, A_{3},…A_{6}. - Now remove the ruled sheet.

**Observation**

7 equal parts will be obtained.

PA_{1} = A_{1}A_{2} = A_{2}A_{3} = A_{3}A_{4} = A_{4}A_{5} = A_{5}A_{6} = A_{6}Q.

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**

- 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.
- Take any rectangular sheet of 5 cm by 9 cm and divide the edges of sheet in 8 equal parts.
- 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 ?

**Answer:**

Two distinct lines which are not intersecting are called as parallel lines.

**Question 2.**

What is transversal line ?

**Answer:**

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

**Question 3.**

What is intercept?

**Answer:**

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 ?

**Answer:**

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 ?

**Answer:**

Line segment is a part of a line.

**Question 6.**

What do you mean by fractions ?

**Answer:**

Equal parts of a whole are called fractions.

**Question 7.**

What do you mean by equivalent fractions ?

**Answer:**

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 ?

**Answer:**

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 ?

**Answer:**

7 folds.

**Question 10.**

Explain the trisection of a strip.

**Answer:**

A strip is divided into three equal parts.

**Question 11.**

Explain the six equal divisions of a rope.

**Answer:**

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?

**Answer:**

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

**Answers**

- (i)
- (ii)
- (i)
- (i)
- (iii)
- (ii)
- (ii)
- (i)
- (i)
- (i)

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