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Procedure
• 1. Draw two points on a piece of paper. To draw a point make a dot on the paper as if you were dotting the letter i.
• 2. Draw a line through these two points. Now draw another line through these same two points. Is that even possible? Draw a third line through these two points. Are the three lines the same of different?
• 3. Draw another two points. How many different lines can you draw through these two points?
Procedure1. Form a ball of clay (your point) the size of a small orange.2. Stick the pointed end of two sharpened pencils (your lines) one inch
into the ball of clay.3. Turn the ball of clay so that both erasers touch the table (your
plane) at the same time.4. Remove the pencils and place them point first into the ball of clay in
a different way. Turn the ball so that both erasers touch the table at the same time.
5. Stick a third pencil into the ball of clay.6. Turn the ball of clay so that all three erasers touch the table at the
same time.7. Remove all three pencils from the ball of clay and place them point
first in the ball of clay in a different way. Find a way to touch all three erasers to the table at the same time.
8. Now stick four sharpened pencils in the ball of clay. Is it possible to turn the ball of clay so that all four erasers touch the table at the same time?
9. Remove all four pencils and place them point first in the ball of clay in a different way. Is there a way to touch all four erasers to the table at the same time?
10.Place the four pencils in the ball of clay so that is it impossible for all four erasers to touch the table at the same time.
Something to think about
• How many legs must a stool have so that it does not tip over?
• How many legs must a stool have to guarantee it always makes solid contact with the floor?
• Did you ever sit in a wobble chair? Why was that?
Procedure
1. Place two pencils on a table. The table represents a plane.
2. Let the two pencils represent two straight lines, but remember that straight lines extend infinitely. Make an X with the pencils. The pencils now intersect at exactly one point.
3. Try to make the pencils intersect at more than one point. It’s impossible! The only way to make two pencils intersect at more than one point is to put them on top of each other, but then they represent the same line.
Postulate
• A line contains at least two points; a plane contains at least three points not all in one line; space contains at least four points not all in one plane
Experiment 1 = Postulate
• Through any two points there is exactly one line
•What does this postulate mean?•You can draw many lines through a single point•Two points determine a single line•You can draw one line through any two different points
Experiment 2 = Postulate
• Through any three points there is at least one plane, and through any three non collinear points there is exactly one plane.
What does this postulate mean?•Through a single point there are an infinite number of planes.•Through two points you can also find an infinite number of planes.•Through three points that lie in a straight line there are an infinite number of planes.•Through three points that do not lie in a straight line there is only one plane.
Postulate
• If two points are in a plane, then the line that contains those points is in that plane.