Geometry Honors Summer Work
1. How long is the shortest path from
one corner of a cube (with each edge
exactly one inch long) to the
opposite corner (e.g., from A to G)?
(Hint: The shortest path does not
follow along an edge at any point.)
2. How long is the shortest path from
one corner of a rectangular box (5 in
wide, 4 inches deep, and 3 inches
high) to the opposite corner? How
precise is your answer?
3. In the figure below you see two
squares attached to each other. Cut
out the shaded figure (do not cut along the segment where the two original
squares meet). Then cut along the dotted line segments. Can you rearrange
the three pieces so that they form a new square? Try to write down a
procedure to do that that you could explain over the telephone (no video
chat).