GEOMETRIC REASONING

​Activity 1: Need for Proof

Task 1

Mark 2 distinct points on a circle and join them.
Note how many separate regions the circle is divided into

• Number of points on circle : _____
• Number of separate regions : _____

Task 2

• Number of separate regions : _____
• No of points on the circle_____

Task 3

Mark 4 distinct points on one circle, join all possible pairs of points.
Note the number of (separate) regions. In the other circle, do the same with 5 distinct points.


For four distinct points on the circle-

• Number of points on circle: _____
• Number of separate regions: _____

For five distinct points on the circle-

• Number of points on circle: _____
• Number of separate regions : _____

Task 4

Now record your observations from Tasks 1-3 in the table given below.

Task 5

What is the pattern you observe? Write it down. (You could write it as a ‘rule’ about the relationship between the number of points taken on the circle, and the number of separate regions the circle is divided into.)

_____________________________________________________________

_____________________________________________________________

Task 6

Task 7

Verify your ‘rule’ by taking:

i) 1 point on a circle
Number of separate regions: ___

ii) 6 points on a circle
Number of separate regions: ____

Task 8

Does your rule hold true? Based on this, would you like to change your response to Task 7?
If yes, put the new response here.

_____________________________________________________________

_____________________________________________________________​

Think about this!
How many examples do you think are ‘enough’ to prove a conjecture?
How many examples do you think are ‘enough’ to disprove a conjecture?