Geometric Postulates Flashcards
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Questions and Answers

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?

  • 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?

  • 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?

    <p>Postulate 2: Through any two different points, exactly one line exists.</p> Signup and view all the answers

    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.

    <p>Postulate 3: Through any three points that are not one line, exactly one plane exists.</p> Signup and view all the answers

    What is the postulate that verifies that line segment AB is in plane Q when points A and B are in Q?

    <p>Postulate 4: If two points lie in a plane, the line containing them lies in that plane.</p> Signup and view all the answers

    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?

    <p>Postulate 1a: A plane contains at least three points not all on one line.</p> Signup and view all the answers

    How many lines are determined by two points?

    <p>1</p> Signup and view all the answers

    Which of the following cannot be used to state a postulate?

    <p>theorems</p> Signup and view all the answers

    Which of the following requires a proof?

    <p>theorem</p> Signup and view all the answers

    Two planes intersect in exactly _____

    <p>one line</p> Signup and view all the answers

    If a ray lies in a plane, how many points of the ray are also in the plane?

    <p>all of the points</p> Signup and view all the answers

    If C is between A and B then AC + CB = AB.

    <p>always</p> Signup and view all the answers

    Three points are collinear.

    <p>sometimes</p> Signup and view all the answers

    Two planes intersect in exactly one point.

    <p>never</p> Signup and view all the answers

    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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    Description

    Test your understanding of essential geometric postulates with this set of flashcards. Each card presents a question about key postulates that underpin the foundations of geometry. Reinforce your knowledge and prepare for your geometry class or exam.

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