
Question: 1
How would you rewrite Euclid’s fifth postulate so that
it would be easier to understand?
Solution:
Euclid’s fifth Postulate:
If a straight line, falling on two straight lines, makes
the interior angles on the same side of it taken together
less than two right angles, then the two straight lines,
if produced indefinitely, meet on that side on which
the sum of angles is less than two right angles.
Interpreting the fifth postulate:
a) If two lines are parallel to each other and a line is
drawn intersecting the two parallel lines, then the
sum of the two interior angles that this line makes with
the parallel lines is equal to two right angles
.
b) If a line intersects two lines, and the sum of the two
interior angles that this line makes with the parallel
lines is less than two right angles, then the two lines
that are intersected are not parallel to each other.