Back to Lesson 9-2
Three-Dimensional Figures
Lesson 9-2
7. The bases of a cube are squares, which are
regular quadrilaterals. Thus, a cube is a
regular prism.
(pp. 525–531)
Mental Math
a. 38
8. oblique decagonal prism
b. yes
9.
20˚
c. 8
Activity
Step 1.
10.
70˚
P
11. The amount of lean plus the measure of the angle
of the lateral edge equals 90°.
Steps 2, 3.
12. 10 √
2 cm ≈ 14.14 cm
Name
Pentagonal Prism
Hexagonal Prism
Octagonal Prism
n-gonal Prism
Faces
7
8
10
n+2
Vertices
10
12
16
2n
Edges
15
18
24
3n
Step 4.
13. a. 64
b. 4 √
3 ≈ 6.9
14. a. 16
b. 36
15. about 9.6 in.
A 100-gonal prism has 102 faces, 200 vertices,
and 300 edges.
16. a. 8
b. 2 or 4
Questions
1. A surface separates space into two regions, an
interior and an exterior. A solid is the union of a
surface and its interior.
b. AFB and DEC
c. False; if the base is not a regular polygon, the
lateral faces may not be congruent.
c. triangular prism
___ ___ ___ ___ ___ ___ ___ ___
___
e. AF, FB, BA, DE, EC, CD, AD, FE, and BC
3. ABCDEF and QRSNOP, FEOP and BCSR, AFPQ
and CDNS, EDNO and ABRQ
___ ___
___
4. CB, OP, and SR
17. a. True; every lateral edge is produced by
equivalent translations of points.
b. False; the lateral edges of an oblique prism are
not perpendicular to the bases.
2. a. cylindrical solid
d. AFED, FBCE, and BADC
c. parallelograms or squares
d. True; the lateral faces of a prism always
have four sides; thus, the bases must be
quadrilaterals for every face to be congruent.
The bases must also be regular polygons and
the prism right. These conditions are satisfied
only by a cube.
5. true
18. 6
6. C
19. 12s
A162
Geometry
Back to Lesson 9-2
20. a.
p
m
26. Answers vary. Sample:
(1) movement to the side; seen horizontally, the
translation vector creates the lateral sides by
moving a base from top to bottom.
(2) pertaining to or at the side; a lateral side is on
the side of a prism when considering the bases
as the top and bottom.
b.
m
p
c.
p
m
21. The line and the plane are perpendicular.
15π+2
22. ______
2
23. a. no
b. Answers vary. Sample:
24. a. v must be either in the same or opposite
.
direction of AB
b. The magnitude of v must
___ be less than or
equal to the length of AB.
A163
Geometry
25. Answers vary. Sample: Light passing through
a prism refracts, that is, it bends away from
its original trajectory. Because refraction is
wavelength-dependent, white light passing
through a prism will disperse, resulting in a color
spectrum.