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Math Help - proving congruncy

  1. #1
    Member helloying's Avatar
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    proving congruncy

    i cant prove part(b). i think since ABCD is rectangle and not square, Ab is not equal to BC. this means the two triangle cannot be the same.pls help me thanks
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  2. #2
    MHF Contributor Amer's Avatar
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    Quote Originally Posted by helloying View Post
    i cant prove part(b). i think since ABCD is rectangle and not square, Ab is not equal to BC. this means the two triangle cannot be the same.pls help me thanks

    take the two triangles ABC and the triangle PBQ we have

    AB = PB cuz ABP equilateral triangle
    BC = BQ cuz BCQ equilateral triangle and
    <ABC = < PBQ = 90

    the two triangles congruent with SAS side-angle-side in the result you have
    AC=PQ
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  3. #3
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    Quote Originally Posted by helloying View Post
    i cant prove part(b). i think since ABCD is rectangle and not square, Ab is not equal to BC. this means the two triangle cannot be the same.pls help me thanks
    A rectangle may be square; it may have equal sides.
    A square can ONLY have equal sides.

    A square is included in the definition of rectangle.
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  4. #4
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    draw AC and PQ
    angle ABC = angle PBQ = 90
    AB = CB
    PB = QB
    hence triangle ABC congruent PBQ (SAS)
    hence AC = PQ
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  5. #5
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    Quote Originally Posted by ukorov View Post
    draw AC and PQ
    angle ABC = angle PBQ = 90
    AB = CB
    PB = QB
    hence triangle ABC congruent PBQ (SAS)
    hence AC = PQ
    sorry...mistake:
    AB = PB
    CB = QB
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