An activity : Deducing Angles

All the angles in the shapes folded from A paper can be deduced using a simple series of formal reasoning based on practical experience.

This provides a practical an interesting exercise in thinking, explaining and justifying.

Activity 1

Start with Kite 1. Challenge pupils to work out what the size of each angle using as a starting point that the angles of the rectangle are 90 degrees. Encourage them to use reasons based on

a) what they did to create each shape

b) the matching of angles.

The comments give an idea of the kind of explanations children will give.

“ The angle at the bottom of the kite was made by folding the 90 degrees in half. So each must be 45 degrees.”

“This corner is 90 degrees. Its just one of the corners of the right angle!”

“The top corner is made from an angle of 45 and an angle of 90. So it must be 135 degrees”.

“This corner is made from two angles of 45 degrees so it must be 90 degrees. Look I can place a 90 degree corner on top and it matches!”.

Activity 2

Now let students look at the Isosceles Triangle.

Unfold it and see if this helps you…..and use the kite you already know about if you like.

“The top angle must be 45. We folded 90 in half to get it”

“This angle is 135degrees (180 – 45). We folded across it to make the bottom angle of the triangle so it must be 67.5”

“I put two of the triangles together like this.

The angle they make matches the top angle of the kite.. so it is 135.

So each one must be half this”

Activity 3

Now look at Kite 2.

As a further exercise open up the kite completely and look at all the angles made by the creases. Can you work them out?

All the angles can be deduced from the folds used or by using the angles already discovered in the first two shapes.