Euclid's Five Postulates Exploration
Materials needed: a few sheets of paper, pencil, ruler, compass
- Draw two dots in the middle of a sheet of paper. Connect them using a straight line.
- Can you draw a different straight line between the same two points? Why?
- Can you extend that line?
- If the paper is infinite, would the line have to stop or curve? Why?
- Using the line drawn between the two dots as a radius, draw a perfect circle. How do you know if the circle is perfect?
- Take another sheet of paper. Tear out a large irregular shape.
- Fold the paper once (anywhere).
- Fold the paper a second time so that the first fold line lies exactly on top of itself.
- Now you have a perfect right angle at a corner of your folded paper. Label it. Compare your 'folded' right angle with your friend's. They are different pieces of paper and were folded in different places. Why does the angle look the same?
- Take another sheet of paper, draw a straight line and a single point not on that line.
- Using a ruler, draw a straight line through point that will never touch line . How do you know they will never touch?
- Now, can you draw a different line through point that will also never touch line . What conclusion can you make?
Compare your answers with the following postulates by Euclid.
- Two points can only be joined with one straight line segment.
- Any straight line segment can be indefinitely extended.
- Given any straight-line segment, there is exactly one circle with the segment as a radius and one endpoint as its center.
- All right angles are congruent.
- Only one line can be drawn parallel to a given line through a given point, not on a given straight line.