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Math Help - True/False and Fill in the Blank statements confusing!

  1. #1
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    True/False and Fill in the Blank statements confusing!

    True or False? (these are confusing me...am i right for the ones I answered?)

    -7 is a square root of 49 F

    |-x|=|x| T

    If PQ = QR, then Q is the midpoint of segment PR.

    If a segment is entirely contained in S, then S is a convex set.

    If A, B, and C are three collinear points and AB<AC, then A-B-C

    On the line PR the coordinate of point P is 17 and the coordinate of R is -6. Then PR = |17-6|. T

    If two planes are not parallel, they must intersect T

    If three points are collinear, they are coplanar T

    A point and a line always lie in exactly one plane. F


    Fill in the blank w/ always, never, or sometimes (answers by me are bolded)

    Two points sometimes lie in exactly one plane
    Two intersecting lines sometimes lie in exactly one plane
    Two lines that are not coplanar never intersect
    A half plane never contains its edge
    Four points, three of which are collinear, are never coplanar
    Three lines intersecting in one point are sometimes coplanar

    Are rays, lines, squares, planes, and circles all a convex set? YES <--- is that right?
    The intersection of two rays may be a segment? line? ray? point? an empty set? point <--- is that right and is it only a point or can it be something else?
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  2. #2
    Super Member Matt Westwood's Avatar
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    Quote Originally Posted by EyesThatSparkle02 View Post
    True or False? (these are confusing me...am i right for the ones I answered?)

    -7 is a square root of 49 F

    |-x|=|x| T

    If PQ = QR, then Q is the midpoint of segment PR.

    If a segment is entirely contained in S, then S is a convex set.

    If A, B, and C are three collinear points and AB<AC, then A-B-C

    On the line PR the coordinate of point P is 17 and the coordinate of R is -6. Then PR = |17-6|. T

    If two planes are not parallel, they must intersect T

    If three points are collinear, they are coplanar T

    A point and a line always lie in exactly one plane. F


    Fill in the blank w/ always, never, or sometimes (answers by me are bolded)

    Two points sometimes lie in exactly one plane
    Two intersecting lines sometimes lie in exactly one plane
    Two lines that are not coplanar never intersect
    A half plane never contains its edge
    Four points, three of which are collinear, are never coplanar
    Three lines intersecting in one point are sometimes coplanar

    Are rays, lines, squares, planes, and circles all a convex set? YES <--- is that right?
    The intersection of two rays may be a segment? line? ray? point? an empty set? point <--- is that right and is it only a point or can it be something else?
    These are the ones which need comment, the others are okay.

    -7 is a square root of 49 F - No it's true.

    If PQ = QR, then Q is the midpoint of segment PR. - Not necessarily, only if P, Q, R are on the same line. If PQR is an isosceles triangle it's false.

    If a segment is entirely contained in S, then S is a convex set. - Not necessarily. If all line segments whose start and end points are in S are completely in S, then S is convex.

    If A, B, and C are three collinear points and AB<AC, then A-B-C
    - This is not a complete statement.

    On the line PR the coordinate of point P is 17 and the coordinate of R is -6. Then PR = |17-6|. T
    - Again this appears incomplete, I can't see how "17" and "-6" are complete definitions of co-ordinates.

    A point and a line always lie in exactly one plane. F
    - Actually this is true.

    Two points sometimes lie in exactly one plane
    - Never. There is always an infinite number of planes containing the line joining two points. At least in 3 or more dimensions.

    Two intersecting lines sometimes lie in exactly one plane
    - Always, at least in 3D.

    A half plane never contains its edge
    - Sorry, not sure whether this is true or not.

    Four points, three of which are collinear, are never coplanar
    - No, the answer's "always".

    Not sure about the last two in your list, I'm out of practice with these geometrical definitions.
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  3. #3
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    A half plane never contains its edge
    False. For an "open" half plane, this is true. For a "closed" half plane it is false. Just "a half plane" includes "closed" half plane so false.

    Four points, three of which are collinear, are never coplanar
    This is false. The three which are collinear give you a line. If the fourth point is not on that line, the four points determine a unique plane. If the fourth point does lie on that same line, there are an infinite number of planes through but in any case they are always "coplanar".
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  4. #4
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    A half plane never contains its edge
    Quote Originally Posted by HallsofIvy View Post
    False. For an "open" half plane, this is true. For a "closed" half plane it is false. Just "a half plane" includes "closed" half plane so false.
    There needs to be a word of caution here. That definition really depends on which textbook is in use.
    In all of the Axiomatic Geometry texts that I have used, the definition of half-plane always excludes the edge from the set.
    Last edited by Plato; October 8th 2009 at 01:49 PM.
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