Sunday, May 18, 2008

Elearn Geometry Problem 7

Geometry Problem, Triangle, Angles

See complete Problem 7 at:
www.gogeometry.com/problem/problem007.htm

Triangle, Cevian, Angles, Congruence. Level: High School, SAT Prep, College geometry

Post your solutions or ideas in the comments.

11 comments:

  1. trazar la ceviana exterior BE (que corta a la prolongacion de AC en E)
    Si el angulo EBC=x
    entonces el angulo BEC=3x...(1)
    Ademas los triangulos ABC y BED son congruentes
    y de (1) se tiene que: el angulo ABC=3x
    Finalmente en el triangulo ABC
    3x+4x+3x=180º
    10x=180º
    x=18º

    atte:tino

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  2. http://geometri-problemleri.blogspot.com/2009/10/problem-34-ve-cozumu.html

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  3. http://ahmetelmas.files.wordpress.com/2010/05/cozumlu-ornekler.pdf

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  4. Given:
    ABC=A+B+C
    ABC=180 A=3x B=x+2x C=4x
    Solution:
    ABC=A+B+C
    180=3x+x+2x+4x
    180=10x
    180/10=10x/10
    18=x

    answer:
    A=3x B=x+2x C=4x
    A=3(18) B=18+2(18) C=4(18)
    A=54 B=18+36 C=72
    B=54

    180=54+54+72
    180=180

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  5. To Jonathan (Problem 7): Why B=x+2x?

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  6. Video-solution to the problem by me:

    http://www.youtube.com/watch?v=cMkCjlKlgRk

    Greetings.

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  7. The solution is uploaded to the follwing link

    https://docs.google.com/open?id=0B6XXCq92fLJJLWMyd3E5THpTTTJKZHdOaVU2UjRzZw

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    Replies
    1. Triangles in the first step can not be congruent by AAS
      there is no criteria of AAS for congruence

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    2. There is no rule of AAS congruence, side common between angles must be same...................

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  8. Sea E el punto en la prolongación de A-C tal que CE = AD
    Sea F tal que F-E es paralela a D-B y además EF=DB
    Con esto se arma un rombo DBFE
    La diagonal B-E corta a C-F en un punto G
    Esta diagonal también es bisectriz por lo que ang(GEC)=3α, lo que hace que
    △CGE y △BGF sean isósceles.
    Como BFEC es un paralelogramo recto se deduce que:
    ang(ECB) = ang(FEC)
    Pero esto implica:
    6α=180°-4α
    α=18° Q.E.D.

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  9. Construct isoceles Tr. ABE where E is on AC. Then Tr. BDE is isoceles and so DE = BD= AC

    Hence Tr.s ABC & BED are congruent SAS from which it follows that Tr. BDC is isoceles with internal angles adding upto 10x and so x=18

    Sumith Peiris
    Moratuwa
    Sri Lanka

    ReplyDelete