```William R. Colson - Morgan Park High School

Corresponding terms (examples):

Euclidean                     Spherical
point                         same ("polar" points are endpoints of a
diagonal of the sphere)
line                          great circle
plane                         sphere
ray                           none
line segment                  arc of a great circle
angle                         angle (intersection of two arcs)

List #2
Corresponding statements (examples):

1) E: There is a unique straight line passing through any two points.
S: There is a unique great circle passing through any pair of nonpolar
points.
2) E: If three points are collinear, exactly one lies between the other two.
S: If three points are collinear, any one of the three points is between
the other two.
3) E: The intersection of two lines creates four angles.
S: The intersection of two great circles creates eight angles.
4) E: If two lines are parallel to a given line, they are parallel to each
other.
S: There exist no parallel lines.

Performance Assessment:1) Individual responses when matching corresponding terms.2) Group discussion and presentation of corresponding statements.3) Group discussion and presentation or individual write-up of conjecture    reached in follow-up activity. Conclusions:Depends on particular content chosen.  In general, they should conclude that most, but not all, terms and properties in Euclidean geometry have counterparts in spherical geometry.  More advanced students may be asked to discover properties unique to spherical geometry.```