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Euclid's 5th Postulate:
1. Euclid's first four postulates are simple and straightforward, but the 5th is quite cumbersome: (from Sir Thomas L. Heath's 1952 translation from the Greek)
| Let the following be postulated: That, if a straight line falling on two straight lines make the interior angles on the same side less than two right angles, the two straight lines, if produced indefinitely, meet on that side on which are the angles less than the two right angles. |
What are some questions you have about this clumsy statement!?
Read Definition 10 of Euclid. What does the expression, "make the interior angles on the same side less than two right angles," mean?
Draw a representation of the long statement above, Euclid's 5th Postulate. Label the interior angles to which the statement refers.
Construct a Sketchpad diagram to illustrate the 5th Postulate, and print it.
2. Reproduce the diagram below using Sketchpad. Referring to the notation used in the diagram, suppose that the angles ABC and BCD are greater than two right angles. What can you conclude about angles FBC and BCE? Explain your reasoning.
What can you conclude about segments ED and FA? Why?