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.
CBSE Class 9 Maths Lab Manual – Mid-point and Perpendicular Bisector of a Line Segment 1
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.
CBSE Class 9 Maths Lab Manual – Mid-point and Perpendicular Bisector of a Line Segment 2

Materials Required
Tracing papers, geometry box, a pair of scissors.

Procedure

  1. Take a square sheet of tracing paper and draw a line segment PQ of desired length as shown in fig. (i).
    CBSE Class 9 Maths Lab Manual – Mid-point and Perpendicular Bisector of a Line Segment 3
  2. Fold this sheet along the middle in such a way that point P falls on point Q fig.(ii).
    CBSE Class 9 Maths Lab Manual – Mid-point and Perpendicular Bisector of a Line Segment 4
  3. 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).
    CBSE Class 9 Maths Lab Manual – Mid-point and Perpendicular Bisector of a Line Segment 5

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

  1. Take a piece of tracing paper and draw a line segment PQ of desired length as shown in fig.(i).
    CBSE Class 9 Maths Lab Manual – Mid-point and Perpendicular Bisector of a Line Segment 3
  2. 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
    CBSE Class 9 Maths Lab Manual – Mid-point and Perpendicular Bisector of a Line Segment 7
    CBSE Class 9 Maths Lab Manual – Mid-point and Perpendicular Bisector of a Line Segment 8
  3. Open the paper, a crease is formed at M. Draw a dotted line on this crease with pencil and name it as ML.
    CBSE Class 9 Maths Lab Manual – Mid-point and Perpendicular Bisector of a Line Segment 9
    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.
  4. 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.
  5. Join M and M’. MM’ is perpendicular to PQ.
    CBSE Class 9 Maths Lab Manual – Mid-point and Perpendicular Bisector of a Line Segment 10

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

  1. Take any triangle and draw perpendiculars from the opposite vertex to corresponding side of a triangle.
  2. Take any triangle and find the mid-points of three sides by paper folding activity.
  3. 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.
CBSE Class 9 Maths Lab Manual – Mid-point and Perpendicular Bisector of a Line Segment 11
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

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

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