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Activities

Exploring lines I

Background

Lines are formed when two surfaces meet. They are also formed when you fold a paper (a plane surface). Lines can also be drawn on paper. Lines can be straight or curved. Lines by definition extend in both directions indefinitely; we say they are of infinite length. For practical purposes we consider pieces of a line; we call them line segments. For this activity, you can use a number of broom-sticks, bicycle spokes or pieces of thread to make lines. You can also use lines drawn on transparent plastic sheets.

Rays are line which can be thought of as starting from a point and proceeding for ever on the other side. Thus a ray is a line that has a definite starting point but is of indefinite length.

Aim

To distinguish between straight and curved lines.

To recognise parallel, collinear and intersecting lines.

To construct lines meeting given conditions.

Activities

Mark a point on the ground or on a piece of paper. Call it A. Construct a ray that starts from A. How many rays can you construct?

Mark two points A and B on paper or on the ground. How many rays can you draw that starts at A and passes through B?

Mark three points A, B, C such that they are not on a straight line. Starting from A how many rays can you construct that passes through both B and C? Draw two rays, one starting from A and passing through B and the other starting from A and passing through C, you can identify two line segments AB and AC. Of these, which line segment is longer? AB or AC? Mark another point D and construct a line segment AD such that AD is shorter than both AB and AC. Mark a point E and construct a line segment AE such that AE is longer than both AB and AC.

Use broom-sticks or bicycle spokes and make two lines such that they do not cross each other. What happens if we extend the lines in one direction? What happens if we extend them in the other direction? Do they cross each other?

Use two sticks and make them cross each other. Try and make two straight sticks cross each other at more than one point? Can you do it?

Use a thread and make a curved line on the floor or table. Place a straight stick on it. At how many points did the straight line cross the curved line? Try to place the straight stick in such a way that it crosses the curved line in many places. What was the maximum number of points (crosses) you could make?

Use straight sticks and make three lines such that each line cuts the other two. In how many different ways can you do this?

Arrange three straight sticks such that one pair is parallel and the third line cuts them both.

Arrange three straight sticks such that all the three lines cross each other at the same point. Arrange three straight sticks such that they do not cross each other at all. How many different ways can you arrange them?

Related Questions

If two straight sticks appear parallel, how can you use more sticks to demonstrate whether the sticks are parallel or not?

Fold paper to form parallel lines

Fold paper to make intersecting lines.

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