Angles in the same segment

As performed in the real lab:

Materials required:

Coloured papers, pair of scissors, gum, scale, compass, pencil, carbon papers or tracing papers.


1. Draw a circle of any radius with centre O and cut it.
2. Paste the cutout on a rectangular sheet of paper. [Fig 1(a)].
3. Fold the circle in any way such that a chord is made. Draw the line segment AB.
[Fig 1(b)].
4. Take two points P and Q on the circle in the same segment. [Fig 1(c)].
5. Form a crease joining AP. Draw AP. [Fig 1(d)].
6. Form a crease joining BP. Draw BP. [Fig 1(e)].
7. ∠ APB is formed in the major segment. [Fig 1(f)]
8. Form a crease joining AQ. Draw AQ. [Fig 1(g)]
9. Form a crease joining BQ. Draw BQ. [Fig 1(h)]
10. ∠ APB and ∠ AQB are formed in the major segment. [Fig 1(i)]
11. Make replicas of ∠ APB and ∠ AQB using carbon paper or tracing paper.
[Fig 1(j)]
12. Place the cutout of ∠ APB on the cutout of ∠ AQB.


As performed in the simulator:


1) Mark a point on the workbench area such that it forms radius for the circle with point O as the origin.

2) Mark two points A and B on circle to draw chord AB.

3) Mark two points P and Q on the circle in any one of the segment to form ∠APB and ∠AQB.

4) Click on ∠APB to rotate it.

5)  Drag ∠APB and place over ∠AQB such that they overlap each other.



1. ∠ APB and ∠ AQB are angles in the same segment.
2. ∠ AQB covers ∠ APB exactly. Therefore ∠ APB = ∠ AQB.