Class 09 To verify that the angles in the same segment of a circle are equal.

 Activity 23 

OBJECTIVE                                                                     

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

 METHOD OF CONSTRUCTION

MATERIAL REQUIRED 

Geometry box, coloured glazed papers, scissors, cardboard, white paper and adhesive.

 1.   Take a cardboard of suitable size and paste a white paper on it.

 2.   Take a sheet of glazed paper and draw a circle of radius a units on it [see Fig. 1].

 3.   Make a cut-out of the circle and paste it on the cardboard.

 4.   Take two points A and B on the circle and join them to form chord AB [see Fig. 2].

 5.   Now take two points C and D on the circle in the same segment and join AC, BC, AD and BD [see Fig. 3].

 Take replicas of the angles ∠ACB and ∠ADB.

DEMONSTRATION

Put the cut-outs of ∠ACB and ∠ADB on each other such that vertex C falls on vertex D [see Fig. 4]. In Fig. 4, ∠ACB covers ∠ADB completely. So, ∠ACB = ∠ADB.

 OBSERVATION

 On actual measurement:

 ∠ACB = ---------------, ∠ADB = ---------------

 So, ∠ACB = ∠ADB. Thus, angles in the same segment are ---------.

 APPLICATION

 This result may be used in proving other theorems/riders of geometry related to circles.