Aim #5 and HW #5.notebook
February 06, 2017
2) Determine the length of AC' given the dimensions 3 x 4 x 5.
D'
A'
C'
B'
D
A
5
3
B
4
C
3) Indicate whether each statement is always true (A), sometimes true (S), or
never true (N).
a. If two lines are perpendicular to the same plane, the lines are parallel.
b. Two planes can intersect in a point.
c. Two lines parallel to the same plane are perpendicular to each other.
d. If a line meets a plane in one point, then it must pass through the plane.
e. A line and a point not on the line form more than one plane.
4)
In the prism to the left, MA MS, MA MH. Lines
that appear to be parallel are parallel. Which plane is
perpendicular to MA?
(1) MAT
(2) HES
(3) MSP
(4) SPL
5) A base of the 3-dimensional figure to the right is a regular
pentagon. If a plane slices through this figure parallel to the
base, the cross-section formed by the slice is a ____________.
6) In the diagram, line k is perpendicular to plane P at point T.
Which statement is true?
(a) Any point in plane P also will be on line k.
(b) Only one line in plane P will intersect line k.
(c) All planes that intersect plane P will pass through T.
(d) Any plane containing line k is perpendicular to plane P.
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Aim #5 and HW #5.notebook
February 06, 2017
7) Use the diagram to the right for a-e:
a) What can be concluded about the relationship
between line l and plane P? Why?
b) What can be concluded about the relationship
between planes P and Q? Why?
c) What can be concluded about the relationship
between lines l and m? Why?
d) What can be concluded about segments AB and CD?
e) Line j lies in Plane P, and line i lies in plane Q. What can be concluded about the
relationship between lines i and j?
8) Which group of points is not coplanar based on the picture below?
(1) D,A,F,E
(2) F,G,B,A
(3) E,F,G,H
(4) G,B,F,D
9) Lines m and n intersect at point A. Line k is perpendicular to both lines m and
n at point A. Which statement must be true?
(1) Lines m, n, and k are in the same plane.
(2) Lines m and n are in two different planes.
(3) Lines m and n are perpendicular to each other.
(4) Line k is perpendicular to the plane containing lines m and n.
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Aim #5 and HW #5.notebook
February 06, 2017
10. Consider the right hexagonal prism whose bases are regular hexagonal regions.
The top and the bottom hexagonal regions are called the base faces, and the side
rectangular regions are called the lateral faces.
a. List a plane that is || to plane C'D'E'.
b. List all planes shown that are not || to plane
CDD'.
c. Name a line perpendicular to plane ABC.
d. Explain why AA' = CC'.
e. Is AB || to DE? Explain.
f. Is AB || to C'D'? Explain.
g. Is AB || to D'E'? Explain.
h. If line segments BC' and C'F' are perpendicular then is BC' perpendicular to
plane C'A'F'? Explain.
i. One of the following statements is false. Identify which statement is false and
explain why.
a) BB' is perpendicular to B'C'.
b) EE' is perpendicular to EF.
c) CC' is perpendicular to E'F'.
d) BC is || to F'E'.
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Aim #5 and HW #5.notebook
February 06, 2017
Name ______________________
HW #5
CC Geometry H
Date ______________________
A'
1) Use the rectangular prism to answer a-f.
D'
a. To which edges is BB' perpendicular?
b. Name a line that intersects plane ABB'A'.
Name a line that will not intersect.
C'
B'
A
c. Are AB and D'C' coplanar? If yes, shade the plane.
D
300
6
4
d. Can lines AB and B'C' lie in the same plane?
B
C
e. plane ABCD ∩ plane C'D'DC = ________
f. Given CC' = 6 and AB = 4, find BC in simplest radical form.
2) Indicate whether each statement is always true (A), sometimes true (S),
or never true (N).
a. Skew lines can lie in the same plane.
b. If two lines are parallel to the same plane, the lines are parallel.
c. If two planes are parallel to the same line, they are parallel to each other.
d. If two lines do not intersect, they are parallel.
3) In the right triangular prism shown at the right, which planes are parallel?
(1) ECBF and DABF
(2) EDAC and ECBF
(3) ACB and DABF
(4) DEF and ACB
4) Choose all that are true.
a. If two planes are parallel to a third plane, the two planes are parallel.
b. If two planes are perpendicular to a third plane, then the two planes are ll.
c. If a plane intersects two ll planes, then the intersections are two ll lines.
d. If a line is perpendicular to a plane, then every plane containing the line is
perpendicular to the given plane.
5) If two distinct lines are perpendicular to the same plane, then the lines are
(1) collinear
(2) congruent
(3) coplanar
(4) consecutive
6) If three planes intersect as shown, the intersection forms
(1) a line
(2) two lines
(3) a fourth plane
(4) a rectangle
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Aim #5 and HW #5.notebook
February 06, 2017
7) The diagram shows a right rectangular prism determined by vertices A, B, C, D,
E, F, G, and H. Square ABCD has sides of length 5 and AE = 9. Find DF to the
nearest tenth. (Hint: find AF first)
8) In the following figure, ΔABC is in plane P, ΔDEF is in plane Q, and BCFE is a
rectangle. Which of the following statements are true?
a. BE is perpendicular to plane Q.
b. BF = CE.
c. Plane P is parallel to plane Q.
d. ΔABC ≅ ΔDEF.
d. AE = AF.
Review: Find the shaded area to the nearest tenth:
3
6
3
6
5