**CBSE Class 9 Maths Lab Manual – Mid-point and Perpendicular Bisector of a Line Segment**

**Objective**

**(A)** To find the mid-point of a line segment and the perpendicular bisector of a line segment by using paper folding.

**Prerequisite Knowledge**

Definition of mid-point and perpendicular bisector.

**Definition of Mid-point:** A point which divides the line segment into two equal parts is known as a mid-point of a line segment. M is the mid-point of AB.

**Concept of perpendicular bisector:** A line which is perpendicular to the given line segment and divides it into two equal parts is known as perpendicular bisector of the given line segment.

**Materials Required**

Tracing papers, geometry box, a pair of scissors.

**Procedure**

- Take a square sheet of tracing paper and draw a line segment PQ of desired length as shown in fig. (i).

- Fold this sheet along the middle in such a way that point P falls on point Q fig.(ii).

- Press the paper properly, so that a crease is obtained. Unfold the paper and draw the dotted line over the crease.

Name it AB as shown. Name the point of intersection of line AB and PQ as M fig. (iii).

**Observation**

This point M is mid-point of line segment PQ and the crease obtained is perpendicular bisector of PQ.

**Objective**

**(B)** To draw a perpendicular at a point lying on the line segment and from a point lie outside the line segment.

**Materials Required**

Tracing papers, geometry box, a pair of scissors.

**Procedure**

- Take a piece of tracing paper and draw a line segment PQ of desired length as shown in fig.(i).

- Take any point M on the line segment PQ, now fold the paper in such a way that PM falls on MQ as shown in fig.(ii) and fig.(iii).

Press the paper

- Open the paper, a crease is formed at M. Draw a dotted line on this crease with pencil and name it as ML.

**In the same way a perpendicular can be drawn from the point outside the line segment. Hence point M lies outside the line segment PQ.** - On tracing paper, draw figure (v) (a) as shown. Fold the paper along line PQ in such a way that its two opposite corners come close together as shown in (b). Press it and mark the image of point M. Name it M’, unfold the paper.
- Join M and M’. MM’ is perpendicular to PQ.

**Result**

In this way, we find mid-point of line segment and perpendicular bisector of line segment.

**Learning Outcome**

By paper folding activity, students will be able to find the mid-point, perpendicular bisector of any line segment and draw perpendicular from any point lying on or outside the line segment.

**Activity Time**

- Take any triangle and draw perpendiculars from the opposite vertex to corresponding side of a triangle.
- Take any triangle and find the mid-points of three sides by paper folding activity.
- Take any quadrilateral and find the mid-points of four sides by paper folding activity.

**Viva Voce**

**Question 1.**

What do you mean by perpendicular bisector of the line segment ?

**Answer:**

A line which divides the another line segment into two equal parts at 90° is known as perpendicular bisector.

**Question 2.**

How will you differentiate between mid-point and perpendicular bisector of the line segment ?

**Answer:**

A point which divides the line segment into two equal parts is known as mid-point and if a line drawn at the mid-point which is perpendicular to the given line segment is known as perpendicular bisector.

In the adjoining figure M is mid-point of line segment AB and PQ is ⊥bisector of AB.

**Question 3.**

If a line segment of length 8 cm is divided by a perpendicular bisector, then what will be the length of each part of the line segment ?

**Answer:**

4 cm.

**Question 4.**

Is it possible to find the mid-point of a line of 7.3 cm by ruler ?

**Answer:**

No. Because the least count of the ruler is 0.1 cm.

**Question 5.**

What do you mean by median of a triangle ?

**Answer:**

A line passing through the vertex to mid-point of opposite side is called median of a triangle.

**Question 6.**

How many medians can be found in a triangle ?

**Answer:**

Three medians.

**Question 7.**

What is the point of concurrency of medians in a triangle ?

**Answer:**

Centroid.

**Question 8.**

What do you mean by orthocentre ?

**Answer:**

The point of concurrency of three altitudes from vertex to opposite sides in a triangle.

**Question 9.**

How will you find centre of a circle or a circumcircle ?

**Answer:**

By constructing perpendicular bisector of any two chords of the same circle.

**Question 10.**

Name the point of concurrency of three perpendicular bisectors in a triangle.

**Answer:**

Circumcentre.

**Question 11.**

Name the point of concurrency of three altitudes in a triangle ?

**Answer:**

Orthocentre.

**Question 12.**

What is incentre, orthocentre, circumcentre, and centroid in an equilateral triangle ?

**Answer:**

They all lie on the same point.

**Multiple Choice Questions**

**Question 1.**

In what ratio the medians in a triangle divide each other ?

(i) 2:1

(ii) 1:2

(iii) 3:2

(iv) none of these

**Question 2.**

In a right angled triangle, what is the position of

orthocentre ? It lies …………..

(i) inside

(ii) outside

(iii) at the vertex

(iv) none of these

**Question 3.**

Circumcentre of the triangle is the point of concurrency of three ………………

(i) altitudes

(ii) perpendicular bisectors

(iii) angle bisectors

(iv) none of these

**Question 4.**

In a triangle ABC, if AD and BE are two medians intersecting at G. If AG = 3 cm. What is the value of AD?

(i) 4.5 cm

(ii) 6 cm

(iii) 9 cm

(iv) none of these

**Question 5.**

In a APQR, if PM and QN are two medians intersecting at G such that GQ = 5 cm. Find the value of GN.

(i) 7 cm

(ii) 2.5 cm

(iii) 7.5 cm

(iv) none of these

**Question 6.**

In a triangle ‘COW’, CD and WA are two medians intersect at K. If KD = 4 cm, what will be the value of CK?

(i) 5 cm

(ii) 7 cm

(iii) 8 cm

(iv) none of these

**Question 7.**

Where does the orthocentre lie in obtuse angled triangle ?

(i) outside

(ii) inside

(iii) on any side

(iv) none of these

**Question 8.**

If a circumcentre lies on the one side of the triangle then what type of triangle will it be ?

(i) acute angled triangle

(ii) obtuse angled triangle

(iii) right angled triangle

(iv) none of these

**Question 9.**

In an equilateral triangle, the length of each perpendicular bisector will be same or not ?

(i) yes

(ii) no

(iii) two are same

(iv) none of these

**Question 10.**

Where does centroid lie in a right angled triangle ?

(i) inside

(ii) outside

(iii) on the triangle

(iv) none of these

**Answers**

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

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