Lab Manual: Verify that the Angles in the Same Segment of a Circle are Equal | Lab Manuals for Class 9 PDF Download

Objective

Materials Required
Coloured glazed papers, Scissors, Drawing sheet, Geometry box, Sketch pens, Adhesive

Prerequisite Knowledge
(i) All basic informations related to a circle.

(ii) Knowledge about the segment of a circle and angles subtended on it.

Theory

• For basic information related to circle refer to Activity 23.
• 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.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)

Procedure

• Take a piece of cardboard of suitable size and paste a drawing sheet on it.
• From the sheet of glazed paper, cut a circle of radius x units with centre O. (see Fig. 24.3)
  
• Paste the cut out circle on cardboard
• To form chord PQ, take two points P and 0 on the circle and join them, (see Fig. 24.4)
  
• 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)
  
• Now, taking replicas of the ∠PRQ and ∠PSQ. (see Fig. 24.6)
  

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.

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.