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Math Help - cyclic quadrilateral ...

  1. #16
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    Quote Originally Posted by razemsoft21 View Post
    Can you prove that:

    AC is perpendicular to BD
    This is the specific case when angles ADC and ABC are right angles.

    OR

    AC divides BD into 2 equal parts
    Again, those triangles would be right angled.

    OR

    The angels ACB and ACD are equal ?
    Those angles being equal can have the angles ADC and ABC both >90^o

    in which case the quadrilateral would not be cyclic,
    since opposite angles would not necessarily sum to 180^o

    Angles ADC and ABC either have to be right angled, or summing to 180^o

    Having them sum to 180^o is required.
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  2. #17
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    cyclic quardrilateral

    Dear razemsoft,

    If you are interested in a formal proof that your quad is a kite i will respond .But first you must go to google to learn what a kite is and its properties.I make no assumptions in this proof but your kite is not cyclic unless you have extra info to prove that angle D =angle B = 90 degrees



    bjh
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  3. #18
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    Quote Originally Posted by bjhopper View Post
    Dear razemsoft,

    If you are interested in a formal proof that your quad is a kite i will respond .But first you must go to google to learn what a kite is and its properties.I make no assumptions in this proof but your kite is not cyclic unless you have extra info to prove that angle D =angle B = 90 degrees
    Dear bjhopper
    I know the properties of the kite very well, and as you know
    the question is how to prove that the shape is a kite ?
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  4. #19
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    Quote Originally Posted by bjhopper View Post
    Dear razemsoft,

    If you are interested in a formal proof that your quad is a kite i will respond .But first you must go to google to learn what a kite is and its properties.I make no assumptions in this proof but your kite is not cyclic unless you have extra info to prove that angle D =angle B = 90 degrees



    bjh
    It has been shown that the quadrilateral can be cyclic even if those angles are not 90 degrees
    even if someone refuses to see it.
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  5. #20
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    cyclic quadrilateral

    Proof of kite

    Razemsoft's diagram

    Connect DB
    AC must be the perpendicular bisector of DB in order to produce the two equal x angles at A

    AD=AB A is on the perp bisector
    AC=AC x=x AD=AB
    Triangles ADC and ABC are congruent SAS
    Angle D = Angle B CPCT
    Kite is defined


    bjh
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  6. #21
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    Quote Originally Posted by bjhopper View Post
    Proof of kite

    Razemsoft's diagram

    Connect DB
    AC must be the perpendicular bisector of DB in order to produce the two equal x angles at A

    The above line is false

    AD=AB A is on the perp bisector
    AC=AC x=x AD=AB
    Triangles ADC and ABC are congruent SAS
    Angle D = Angle B CPCT
    Kite is defined


    bjh
    Please reference emakarov's diagram earlier in the thread.
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  7. #22
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    I get the point finnally.

    bjh
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