Shape
Copyright David & Cynthia Thomas, 2009
Naming, Describing, and Constructing Polygons--Exercises
Part I
Do the challenge problem and directed activities in this section.
Part II
Complete the following exercises
1. In Table 3.3, there are no entries for the cells labeled 1 pair of parallel sides + 2 pair of congruent sides, 2 pair of parallel sides + no congruent sides, and 2 pair of parallel sides + 1 pair of congruent sides. Explain why.
2. On the basis of the quadrilateral relationships presented in Figure 3.12, justify the following statements.
· Every square is both a rectangle and a rhombus.
· Every rhombus is a parallelogram.
· No trapezoid is a parallelogram.
· No kite is a trapezoid.
3. Create a
rationale (i.e., justification) for the formula for the measure of an interior
angle of a regular n-gon,
.
4. Create and justify a formula for the measure of an exterior angle of a regular n-gon.
5. Complete the following table of features for the indicated regular n-gons.
|
N |
Interior Angle Sum |
Interior Angle |
Exterior Angle |
Exterior Angle Sum |
|
7 |
|
|
|
|
|
9 |
|
|
|
|
|
15 |
|
|
|
|
|
20 |
|
|
|
|
|
36 |
|
|
|
|
|
90 |
|
|
|
|
6. State a conjecture concerning the sum of the exterior angles of every regular n-gon.
7. Using The Geometers Sketchpad, create a model illustrating your conjecture as it applies to a square.
