Euclidean Geometry Answers

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Sample Response: There exists one plane through any three noncollinear points. Since the points cannot be on the same line, at least two lines would have to pass through any of the three points.

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P JB X

A
P
B
J
C
B
D
X
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v xy z

A
v
B
x
C
y
D
z
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Which diagram represents the postulate that states exactly one line exists between any two points?

A
[Image: Point B is on a horizontal line. Point A is above ...]
B
[Image: A diagonal line is shown. Points A and B are not o...]
C
[Image: Points A and B are on a diagonal line....]
D
[Image: Points A and B are shown....]
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In a geometry class, students are asked to describe the dimensions of a plane based on the components that create a plane. Which student’s response is correct?

A
Mark states that a plane has zero dimensions because it is made up of three noncollinear points.
B
Stacy states that a plane has two dimensions because it is made up of an infinite number of lines.
C
Dewayne states that a plane has one dimension because it contains the line intersecting two points.
D
Candice states that a plane can have multiple dimensions depending on how many points are labeled.
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Which statements are true? Select three options.

A
There are exactly two planes that contain points A, B, and F.
B
There is exactly one plane that contains points E, F, and B.
C
The line that can be drawn through points C and G would lie in plane X.
D
The line that can be drawn through points E and F would lie in plane Y.
E
The only points that can lie on plane Y are points E and F.
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