Inductive reasoning can be used in any situation where a pattern is recognizable. The next example uses inductive reasoning to develop conjectures about the differences between categories of geometric shapes. Making conjectures can be very open-ended and as such, it is quite possible that the conjectures you think of will be different than those presented in the example.

Example 5

Make two conjectures about the differences between regular polygons with an even number of sides and regular polygons with an odd number of sides.

When working with geometry it is a good idea to draw diagrams. Begin by drawing some polygons for each category.

Conjecture 1

Step 1
Look for a pattern.

From the diagrams, it looks like there are no parallel sides in polygons with an odd number of sides, while there are multiple pairs of parallel sides in polygons with an even number of sides.

Step 2
Make a conjecture.

Step 3
Check your conjecture.

It is a good idea to test your conjecture using an example from each category.

The conjecture is true for other polygons in each category.

Conjecture 2

Step 1
Look for a pattern.

Sometimes you can do a little exploring and use some creativity to find patterns. For example, drawing a line from each vertex to the centre of the polygon, you can create a series of triangles.

Step 2
Make a conjecture.

Step 3
Check your conjecture.

Again, it is a good idea to test your conjecture using an example from each category.

The conjecture is true for other polygons in each category.

For further information about making conjectures see pages 6–11 of Principles of Mathematics 11.