geometry-labs

3.
Discussion Answers
A.
√5
5
√5
The side of the large square is 45. Its area
is 5 16 80. It follows that 45 80.
4.
B. If the square of m is the greatest square that
is a factor of n, we have n km 2 for some
number k. It follows that a square of area n
could be divided into m 2 squares of area k.
So n mk. (Here, n, m, and k are
positive whole numbers.)
Lab 9.4: Distance from the Origin
Prerequisites: Familiarity with the Pythagorean
theorem, simple radical form, and slope.This lab
makes connections among all these concepts and
works well as a wrap-up report on the work
done in Labs 8.5, 9.1, 9.3, and 9.4.
5. a. 3 2
b. 3 5
c. 2 6
d. 4 2
e. 5 3
f. 7 2
Students may use the records of their work from
Lab 8.5 (Geoboard Squares), but don’t suggest it
if they don’t think of it. Instead, encourage them
simply to apply the Pythagorean theorem many
times.This provides a useful, nonrandom drill.
Working with neighbors and looking for
patterns should speed up the process.
Geometry Labs Notes and Answers 217
© 1999 Henri Picciotto, www.MathEducationPage.org