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Questions and Answers
What is the postulate about two planes?
What is the postulate about two planes?
- Postulate 2: Through any two different points, exactly one line exists.
- Postulate 3: Through any three points that are not one line, exactly one plane exists.
- Postulate 1a: A plane contains at least three points not all on one line.
- Postulate 5: If two planes intersect, then their intersection is a line. (correct)
Which postulate states that a line is determined by two points?
Which postulate states that a line is determined by two points?
- Postulate 2: Through any two different points, exactly one line exists. (correct)
- Postulate 4: If two points lie in a plane, the line containing them lies in that plane.
- Postulate 5: If two planes intersect, then their intersection is a line.
- Postulate 3: Through any three points that are not one line, exactly one plane exists.
Which postulate specifies the minimum number of points in space?
Which postulate specifies the minimum number of points in space?
- Postulate 2: Through any two different points, exactly one line exists.
- Postulate 1b: Space contains at least four points not all on one plane. (correct)
- Postulate 4: If two points lie in a plane, the line containing them lies in that plane.
- Postulate 1: A plane contains at least three points not all on one line.
What is the postulate that states points A and B lie in only one line?
What is the postulate that states points A and B lie in only one line?
Select the postulate that substantiates the fact that a table with four legs can wobble if one leg is shorter than the other three, but a table with three legs will not wobble.
Select the postulate that substantiates the fact that a table with four legs can wobble if one leg is shorter than the other three, but a table with three legs will not wobble.
What is the postulate that verifies that line segment AB is in plane Q when points A and B are in Q?
What is the postulate that verifies that line segment AB is in plane Q when points A and B are in Q?
What is the postulate stating that if G and H are different points in plane R, then a third point exists in R not on line segment GH?
What is the postulate stating that if G and H are different points in plane R, then a third point exists in R not on line segment GH?
How many lines are determined by two points?
How many lines are determined by two points?
Which of the following cannot be used to state a postulate?
Which of the following cannot be used to state a postulate?
Which of the following requires a proof?
Which of the following requires a proof?
Two planes intersect in exactly _____
Two planes intersect in exactly _____
If a ray lies in a plane, how many points of the ray are also in the plane?
If a ray lies in a plane, how many points of the ray are also in the plane?
If C is between A and B then AC + CB = AB.
If C is between A and B then AC + CB = AB.
Three points are collinear.
Three points are collinear.
Two planes intersect in exactly one point.
Two planes intersect in exactly one point.
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Study Notes
Geometric Postulates
- Postulate 5: Intersecting planes will always intersect along a single line.
- Postulate 2: Through any two distinct points, there exists a unique line.
- Postulate 1b: Space must contain a minimum of four points that are not co-planar.
- Postulate 3: A configuration of three non-collinear points determines exactly one plane.
- Postulate 4: If two points lie in a plane, then the line connecting them is also within that plane.
- Postulate 1a: A plane must contain at least three points that are not collinear.
- Two points determine exactly one line.
- Theorems cannot be used to establish postulates; postulates are accepted truths.
- Theorems require formal proofs to validate their statements.
- Two planes intersect in only one line.
- If a ray lies in a plane, every point along that ray also exists in the same plane.
- If point C lies between points A and B, the segment lengths satisfy the equation AC + CB = AB.
- Three points may be collinear under certain conditions, but it is not a necessity.
- It is never true that two planes can intersect at only one point; their intersection is always a line.
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