Answer to Question #108308 in Geometry for Nikita Koladiya

Question

Describe an activity to help children learn that any line may not be an axis of symmetry of a given circle. Give another activity to assess how far the earlier activity was effective for children to understand the axis of symmetry of a circle.

Answer 1

Let's imagine that we have a pizza in front of us. Of course its form is a circle. The problem is to divide pizza by 4 equal pieces. Also, we know a center of our pizza, so all that we need is to cut by straight line which goes through a center. Congrats, we have 2 absolutely identical pieces of pizza (circled form) and a straight line by which we cut is the axis of symmetry of a circle.

We can prove it if we put one piece on second and see if they the same that means all above is true.

But, we remember that we need to cut a pizza into 4 parts, so we take a knife a do the same actions, cut by a straight line which goes through a center. We know we have 4 absolutely equal pieces of pizza.

Suddenly, a lot of friends come to us and we need to give them a piece of pizza of course. We take a knife and cut a pizza by a straight line which goes through a center again and again, so far unexpectedly we are missed and cut by a straight line but which do not go through a center. Well, by our mistake know we do not have equal pieces of pizza because one part will be smaller than another. A line by which we cut the last is the axis of circle BUT not a symmetry because symmetry is when 2 or more shapes are absolutely identical (equal).