Euclid's Five Postulates Exploration
Materials needed: a few sheets of paper, pencil, ruler, compass
- Draw two dots on 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?
- Draw a perfect circle using the connected straight line between the two dots as its radius. How do you know if the circle is perfect?
- Take another sheet of paper and tear it into 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.
- Compare your 'folded' right angle with your friend's. They are different pieces of paper and were folded in different places. If you stack them, do they match perfectly? How do you know?
- Take another sheet of paper, draw a straight line and a single point not on that line.
- Using a ruler, try to draw a line through point that will never touch line .
- Now, try to 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.
- It is possible to draw a straight line segment joining any two points.
- It is possible to indefinitely extend any straight line segment continuously in a straight line.
- Given any straight-line segment, it is possible to draw a circle with the segment as a radius and one endpoint as its center.
- All right angles are equal to each other or congruent.
- Only one line can be drawn parallel to a given line through a given point, not on a given straight line.