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Verify that the Angles in the Same Segment of a Circle are Equal Experiment Class 9 Maths Practical NCERT

The experiment to determine Verify that the Angles in the Same Segment of a Circle are Equal are part of the Class 9 Maths Lab Manual provides practical activities and experiments to help students understand mathematical concepts effectively. It encourages interactive learning by linking theoretical knowledge to real-life applications, making mathematics enjoyable and meaningful.

Maths Lab Manual Class 9 CBSE Verify that the Angles in the Same Segment of a Circle are Equal Experiment

Determine Verify that the Angles in the Same Segment of a Circle are Equal Class 9 Practical

OBJECTIVE

To verify that the angles in the same segment of a circle are equal

Materials Required

  1. Coloured glazed papers
  2. Scissors
  3. Drawing sheet
  4. Geometry box
  5. Sketch pens
  6. Adhesive

Prerequisite Knowledge

  1. All basic informations related to a circle.
  2. Knowledge about the segment of a circle and angles subtended on it.

Theory

  1. For basic information related to circle refer to Activity 23.
  2. The region between a chord and either of its arcs is called a segment of the circular region or simply a segment of the circle. This chord is called the base of the segment.
    NCERT Class 9 Maths Lab Manual - Verify that the Angles in the Same Segment of a Circle are Equal 1
    The segment formed by minor arc along with chord, is called minor segment and the segment formed by major arc is called the major segment.
    If O is the centre of the circle, AB is an arc and P and O are two points on the remaining part of circle. Arc AB subtends ∠APB and ∠AQB in the same segment of the circle. (see Fig. 24.2)
    NCERT Class 9 Maths Lab Manual - Verify that the Angles in the Same Segment of a Circle are Equal 2
    Procedure
  3. Take a piece of cardboard of suitable size and paste a drawing sheet on it.
  4. From the sheet of glazed paper, cut a circle of radius x units with centre O. (see Fig. 24.3)
    NCERT Class 9 Maths Lab Manual - Verify that the Angles in the Same Segment of a Circle are Equal 3
  5. Paste the cut out circle on cardboard
  6. To form chord PQ, take two points P and 0 on the circle and join them, (see Fig. 24.4)
    NCERT Class 9 Maths Lab Manual - Verify that the Angles in the Same Segment of a Circle are Equal 4
  7. Take a pair of points R and S on the circle in the same segment and join RP,RQ, SQ and SP. (see Fig. 24.5)
    NCERT Class 9 Maths Lab Manual - Verify that the Angles in the Same Segment of a Circle are Equal 5
  8. Now, taking replicas of the ∠PRQ and ∠PSQ. (see Fig. 24.6)
    NCERT Class 9 Maths Lab Manual - Verify that the Angles in the Same Segment of a Circle are Equal 6

Demonstration
Put the cut outs of ∠PRQ and ∠PSQ on each other such that vertex R falls on vertex S (see Fig. 24.7). We find, ∠PRQ covers ∠PSQ completely, so ∠PRQ = ∠PSQ.
NCERT Class 9 Maths Lab Manual - Verify that the Angles in the Same Segment of a Circle are Equal 7

Observation
On actual measurement, we get
∠PRQ = ……… ,
∠PSQ = ……… ,
So, ∠PRQ = ∠PSQ.
Hence, the angles in the same segment are ……… .

Result
We have verified that the angles are equal in the same segment of a circle.

Application
This result can be used in proving other theorems/problems of geometry related to circles.

Viva Voce
Question 1:
“The line drawn through the centre of a circle to bisect a chord is perpendicular to the chord”. Is this statement true?
Answer:
Yes

Question 2:
How many longest chords are there in a circle?
Answer:
There are infinite longest chords in a circle passing through the centre and each of them is equal to the diameter of the circle.

Question 3:
What do you mean by the minor segment of a circle?
Answer:
A chord divides a circle into two parts and the smaller part is called the minor segment.

Question 4:
How will you define the major segment of a circle?
Answer:
A chord divides a circle into two parts and the larger part is called the major segment.

Question 5:
How will you relate the angles in the same segment of a circle?
Answer:
Angles will be equal.

Question 6:
Does equal chords of a circle subtend different angles at the centre?
Answer:
No, because equal chords subtended equal angles at the centre.

Question 7:
The angle subtended by an arc at the circle in minor segment is obtuse angle. What is value of angle subtended by it in the major segment?
Answer:
Acute angle

Question 8:
If a chord AB subtended an angle 80° at centre, then what will be the measure of angles subtended by same chord in the same segment of the circle at point P and Q?
Answer:
Chord AB subtended an angle of 40° at both points.

Suggested Activity
To verify experimentally that the angles in the same segment of a circle of radius 6 cm are equal.

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NCERT Class 9 Maths Lab Manual