Multiple Lines & Shapes 1

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Plane Geometry studies the shapes &amp; their properties formed when several lines intersect (or do not) and make several patterns on a plane.

Let us explore further with 2 activities using thin (rigid) plastic sticks or broom sticks instead of lines.

Activity 1

In how many different ways can you place 2 lines (sticks) on a table surface?

Activity 2
 * 1) The sticks should be thought of as extending for ever on both ends.
 * 2) The table surface should also be considered to be extending in all directions so that the edges are not visible.
 * 3) The difference in each way should be deep &amp; logically explainable.

In how many ways can you place 3 lines on a plane surface?

Students should be allowed to work in groups and discuss various possibilities among themselves. Hint – If students have difficulty, they can be asked to think in terms of the number of possible intersections. Most groups should be able to arrive at the solutions, though they may not be able to explain their thinking clearly. Solutions should be discussed only after some time is spent in the assignment.

Solutions should be discussed only after some time is spent in the assignment.

Solutions

Let us first examine the case of 2 lines. There are only 2 ways. This can be summarized as in the table below.

Let us examine the case of 3 lines. There are 4 possibilities as summarized in the table below.

By doing these activities, students would also intuitively understand that on a plane there are no other possibilities.

The above concepts form the foundations of Plane Geometry. They are the beginning topics in the study of Plane Geometry.

We will study each of these in detail in the subsequent chapters.

Chapter 22.8 gives a number of paper folding activities which would help in understanding lines &amp; points.

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