geometry-labs

which Question B hints at, is that by the time
you have walked all around the polygon, your
total turning is 360°.All the other calculations
follow easily from this fact.
If you use spreadsheets or graphing calculators,
you can have students use them to complete
the table; however, that requires figuring out
the formulas.Another approach is to finish
Problem 6 on paper, then extend the table
by using technology.
Question C:The angle sum formula that
flows from Problem 6 is n(180° 360°/n).
This simplifies to 180°n 360°, which can
be factored to the traditional 180°(n 2).
Question D can be the starting point of an
ambitious mathematical research project for
a student, group, or class.
If you have access to the Logo computer
language, your students may follow up this
activity with the equivalent one on the
computer.There, they can explore many
variations of polygon walks. (See almost
any of the books on Logo.) For further
investigations, you could have students use
Logo to write procedures to draw each of
the pattern blocks.A more advanced project
is to combine such procedures to create
pattern block designs on the screen.
Answers
1. Jenny: instructions are ambiguous; Maya: 360°;
Pat: 270°
2. (Take step, turn right 120°) 3
3. 360°
4. a. The interior angles
b. The exterior angles
5. a. Since the polygon is regular, all interior
angles are equal.Therefore, all exterior
angles are equal, and each is equal to the
total turning divided by 7. So each exterior
angle is 360°/7, or approximately 51.43°.
b. Each interior angle is the supplement of
the corresponding exterior angle. In this
case, it is 180° 51.43° 128.57°.
6.
Number Each Angles Turn Total
of sides angle sum angle turning
3 60° 180° 120° 360°
4 90° 360° 90° 360°
5 108° 540° 72° 360°
6 120° 720° 60° 360°
7 128.57° 900° 51.43° 360°
8 135° 1,080° 45° 360°
9 140° 1,260° 40° 360°
10 144° 1,440° 36° 360°
11 147.27° 1,620° 32.73° 360°
12 150° 1,800° 30° 360°
100 176.4° 17,640° 3.6° 360°
n
180° 36 0°
n
Discussion Answers
A. a. Jenny’s instructions are ambiguous.
The other two will yield a square.
b. They all involve taking steps and
turning 90°.
c. Maya’s involve four turns; Pat’s only three.
d. Answers will vary.
e. Answers will vary.
B. Students should agree that total turning is
easiest to find, since it’s always 360°. From
there you can get the turn angle, the interior
angle, and the angles sum, in that order. (See
the formulas in the table above.)
C. Answers will vary.
D. Answers will vary.
n (180° 36 n
0°
) 36 0°
n
360°
Geometry Labs Notes and Answers 181
© 1999 Henri Picciotto, www.MathEducationPage.org