Millau Bridge

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Millau Bridge Sir Norman Foster
Millenium Park Frank Lloyd Wright
Fallingwaters Frank Lloyd Wright
Point, Lines, Planes, Angles
1.5 CE Page 24
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1.5 CE Page 24

1. Theorem 1.1 states that two lines intersect in
   exactly one point. The diagram suggests what
   would happen if you tried to show that 2 lines
   were drawn through 2 points.

State the postulate that makes this situation
impossible.
Through any 2 points there is exactly one line.
2. State postulate 6 using the phrase one and
only one.
Post. 6 Through any two points, there is
exactly one line.
Through any two points, there is one and only one
line.
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3. Reword the following statement as two
statements, one describing existence and one
describing uniqueness.
A segment has exactly one midpoint.
Existence All segments have a midpoint.
Uniqueness A segment has only 1 midpoint.
Postulate 6 is sometimes stated as Two points
determine a line.
4. Restate Theorem 1-2 using the word determine.
Theorem 1-2 If 2 lines intersect, then they
intersect in exactly one point.
If 2 intersecting lines determine one point.
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Postulate 6 is sometimes stated as Two points
determine a line.
5. Do 2 intersecting lines determine a plane?
Yes, there are 3 non-collinear points.
Also Theorem 1-3 states that two intersecting
lines are in exactly 1 plane.
6. Do three points determine a line?
Yes. If the points are collinear then they
determine 1 line. If the points are
non-collinear, then they determine 3 lines.
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7. Do three points determine a plane?
No. If the points are collinear, they dont. If
the points are non-collinear, they do. Sometimes
is always answered NO.
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State a postulate, or part of a postulate, that
justifies your answer for each exercise.
8. Name 2 points that determine line l.
A, C
9. Name three points that determine plane M.
A, B, C also
B, C, D
A, B, D also
10. Name the intersection of planes M and N.
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State a postulate, or part of a postulate, that
justifies your answer for each exercise.
11. Does lie in plane M?
Yes, it is just not drawn.
12. Does plane N contain
any points not on ?
Yes, they are just not drawn or labeled. Each
plane has an infinite number of points.
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13. Why does a three-legged support work better
than one with four legs?
Three legs are always in a plane and therefore
are steady and do not rock. Four points may or
may not be in a plane. Also most ground is not
level.
14. Explain why a four-legged table may rock
even if the floor is level.
The 4 legs may not be in the same plane. Also
over time the four legs move, swell, and are
jarred out of position.
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15. A carpenter checks to see if a board is
warped by laying a straightedge across the board
in several directions. State the postulate that
is related to this procedure.
If there is space under the straight edge,
then the board is curved or warped.
If two points of a line are in the plane, then
the line is in the plane.
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16. Think of the intersection of of the ceiling
and the front wall of your classroom. Let the
point in the center of the floor be point C.
a. Is there a plane that contains line L and
point C?
Yes. Note that this situation has 3
non-collinear points.
L
L
b. State the theorem that applies.
Through a line and a point not on the line, there
is exactly one plane.
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Cest fini.
Good day and good luck.