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Chapter 9 Test
1. The equation for computing the measures of the vertex angles of a regular n-gon
n2180
n
can be written as
. Explain how it is derived.
2. Use Venn diagrams to show the relationship between trapezoids and parallelograms. Explain.
3. A prism has 96 edges. How many vertices and faces does it have? Explain.
4. Given that15° is the measure of a central angle of a regular polygon, explain how you would
determine its number of sides.
5. We know that squares alone will tessellate the plane. We also know that a combination of
squares and regular octagons will tessellate the plane. Explain why these tessellations work,
but regular octagons alone will not tessellate.
6. The corresponding angles property states that m(1) = m(2). Angles 3 and 4 are called
interior angles on the same side of the transversal. Prove that m(3) + m(4) = 180.
1
l ||m
l
3
4
2
m
7. In the following figure, l | | m. Given the angle measures indicated on the figure, find the
measures of the angles identified by a, b, c, d, e, f, and g.
a ______
b ______
c ______
g
e ______
e
m
f _______
g ______
d ______
d
f 132
b
l
101
0
0
610
c
a
8. Donna says she can tessellate the plane with any kind of triangle, but that’s not true for
quadrilaterals, because if you have a concave quadrilateral like the one shown, you can’t do it.
Is she correct? Discuss.
9.
Given a pentagon that showed the measure of four vertex angles, a student was
n2180
n
asked to find the measure of the fifth angle. He said he would use the formula
to find the missing angle. Is he correct? Discuss.
10. How many different line segments are contained in the following portion of a line? Explain.
.
A
.
.
B
.
.
.
C
D
E
F
11. Circle T (true) or F (false).
T
F Every isosceles triangle is equilateral.
T F A tetrahedron has 6 faces, 8 vertices,
and 12 edges.
T
F Every pyramid has a square base.
T F A triangle may have both a right angle
and an obtuse angle.
T F The acute angles of a right triangle are
complementary.
T F The measure of the central angle of a
regular 10-gon is 36°.
T
T
F The supplement of a 75° vertical angle
is 105°.
F A circle is convex.
12. Shown are patterns or nets for several three-dimensional figures. Name the three-dimensional
figure the net forms.
a.
b.
c.
d.
e.
f.
13 In each group, pick one that is different from the others and explain why you picked that one.
There may be more than one way to pick one.
B.
A.
C.
D.
I
B.
A.
C.
D.
L
II
L
L
A.
B.
C.
D.
III
14.
Name the regular polyhedra that have triangular faces.
15
Draw the following. If it is possible, list two significant features; if not possible, explain why.
a. an obtuse right triangle
b. an acute scalene triangle
16.
Explain the difference in a polygon and a polyhedron.
17.
A and B are supplementary angles. Twice the measure of A is one-half the measure of
B. Find the measure of B.
18.
Circle each figure that is a polygon. If a figure is not a polygon, explain why.
19.
A 60-inch piece of pipe is to be cut at two points A and B such that A and B are not the ends of
the pipe. The length from A to B is 42 inches. How many possibilities are there for getting three
pieces of pipe that are all of different lengths? All lengths are whole number of inches. Show strategy.