Angles in the same Segment

OBJECTIVE

To Verify that the Angles in the Same Segment of a Circle are Equal.

PREREQUISITE KNOWLEDGE

Basic terms related to the circle. 

Here, a circle is given O is the centre of the circle

Arc AB subtends ∠APB & ∠AQB in the same segment of the circle.

MATERIALS REQUIRED

Coloured sheet and glazed paper

Tracing paper

Geometry box

Scissors

Adhesive fevicol

PROCEDURE

Take a card board and paste a white paper on it.

Cut a Circle from pink glazed paper of radius a units and centre O

Paste the cut-out ( circle) on the cardboard

                                                                              Image 2

Take two points A & B on the circle and join them to form chord AB

                                                                               Image 3

Again take two points P & Q in the same segment and join AP, BP , AQ and BQ

                                                                            Image 4

Take replicas ( Equal Copy) of ∠APB and  ∠AQB  with the help of tracing paper.

                                                                            Image 5

Now, place the cut-out out of  on t∠APB he cut-out of  ∠AQB  ( P falls on Q)

                                                                              Image 6

OBSERVATION

We observe that ∠APB  covers  ∠AQB completely   (∠APB =∠AQB)

CONCLUSION

Angles in the same segment of a Circle are Equal