Math 102, Activities
Pre-class work: (Read section 9.1, stopping at the subheading “angles” on page 578, which will be a big help answering
the questions below!)
(1) Incidence geometry in two dimensions. True or false? For each assertion, decide whether it is true or false,
then illustrate with a small picture. Each of these statements should be interpreted in the two-dimensional plane.
(a) For any two points, there is exactly one line through them.
(b) For any two lines, there is exactly one point on them.
(c) For any two lines land m, either they are parallel (lkm) or they intersect in just one point.
(d) For any given point, there are infinitely many lines through it.
(e) If four points are arranged in a square and every two are connected with a line, six lines will be formed.
(2) Incidence geometry in three dimensions: True or false? As above, decide whether each is true, and illustrate
with a small picture. Each of these statements should be interpreted in three dimensions. That is, in space.
(a) For any two points, there is exactly one line through them.
(b) It’s possible that three given points could have exactly one line through them.
(c) For any two lines land m, either they are parallel (lkm) or they intersect in just one point.
(d) Two planes can intersect at exactly one point.
(e) Two planes can intersect at exactly one line.
(f) Two planes always intersect at exactly one line.
(g) If two lines intersect, then they are coplanar.
