Ac1.5bPracticeProblems
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Transcript of Ac1.5bPracticeProblems
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Millau BridgeSir Norman Foster
Point, Lines, Planes, Angles
FallingwatersFrank Lloyd Wright
Millenium ParkFrank Lloyd Wright
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.
Existence: All segments have a midpoint.
Uniqueness: A segment has only 1 midpoint.
A segment has exactly one midpoint.
Postulate 6 is sometimes stated as “Two points determine a line.”
4. Restate Theorem 1-2 using the word determine.
Theorem 1-2If 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?
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.
Yes, there are 3 non-collinear points. Also…Theorem 1-3 states that two intersecting lines are in exactly 1 plane.
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7. Do three points determine a plane?
No. If the points are collinear, they don’t. 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.
N
Ml
A
D
C
B
8. Name 2 points that determine line l.
9. Name three points that determine plane M.
10. Name the intersection of planes M and N.
A, C
A, B, C alsoA, B, D also B, C, D
AB�������������� �
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State a postulate, or part of a postulate, that justifies your answer for each exercise.
N
Ml
A
D
C
B
11. Does lie in plane M?
12. Does plane N contain
AD�������������� �
AB�������������� �
any points not on ?
Yes, it is just not drawn.
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?
14. Explain why a four-legged table may rock even if the floor is level.
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.
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 two points of a line are in the plane, then the line is in the plane.
If there is space under the straight edge, then the board is curved or warped.
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CC
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?
b. State the theorem that applies.
Through a line and a point not on the line, there is exactly one plane.
Yes. Note that this situation has 3 non-collinear
points.
L L
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C’est fini.
Good day and good luck.