Sunday, November 20, 2011

Problem 691: Isosceles Triangle, 80-80-20 Degrees, Angles, Congruence, Mind Map, Polya

Geometry Problem
Level: Mathematics Education, High School, Honors Geometry, College.

Click the figure below to see the complete problem 691.

Online Geometry Problem 691: Isosceles Triangle, 80-80-20 Degrees, Angles, Congruence, Mind Map, Polya.

Posted by Antonio Gutierrez at 8:46 AM
Labels: , , , , ,

10 comments:

  1. EditorNovember 20, 2011 at 9:00 AM

    This is far easy one!
    AC=CB and AE perpendicular to DC, then ACED is a deltoid so <CDE=30.
    x=50-30=20 and we are done here (:

    ReplyDelete
  2. Peter TranNovember 20, 2011 at 5:04 PM

    http://img191.imageshack.us/img191/4097/problem691.png
    Since triangle ABC is isosceles so (BAC)=(BCA)=80
    And (DAE)=40 and (DCE)=30
    Triangle DAE congruent to Tri. CAE ( case SAS)
    So DE=EC and ( CDE)=(ECD)=30
    In triangle DAF, x=180-80-80=20
    Peter Tran

    ReplyDelete
  3. MarkovNovember 20, 2011 at 5:20 PM

    Sí pero yo creo que quisiste decir que AC = AD o no?

    ReplyDelete
  4. EditorNovember 21, 2011 at 7:07 PM

    AC=AD, efectivamente. gracias @Markov

    ReplyDelete
  5. Eder Contreras OrdenesDecember 17, 2011 at 7:53 AM

    <ADC is an exterior angle, then tr ADC is isosceles, so we have AD = AC, cause this triangles CAE and DAE are congruents by SAS.
    Then ADF is 80 80 20 , therefore x=20

    Greetings ^^

    ReplyDelete
  6. Sumith PeirisAugust 17, 2015 at 3:36 AM

    AE is easily seen to be the perpendicular bisector of DC hence Tr. DEC is isoceles and < CDE = 30 and so x= 20

    Can anyone show that Tr. BEF is isoceles?

    Sumith Peiris
    Moratuwa
    Sri Lanka

    ReplyDelete
    Replies
    1. GMACDecember 4, 2015 at 12:11 PM

      Using symmetry, <CEF and <DEB are 60 each. Since <BDE is 100 and <CEF is 100 by difference (180- 60-20). Therefore, TR DEB is congruent to Tr ECF (ASA). Since corr sides of cong Tr are equal, EF = EB making TR BEF isoceles.

      Delete
  7. Sumith PeirisAugust 17, 2015 at 3:37 AM

    ....and that BD = CF?

    ReplyDelete
  8. Sumith PeirisAugust 17, 2015 at 3:39 AM

    ...also that AE is perpendicular to BF?

    ReplyDelete
  9. Geek37November 7, 2018 at 11:02 AM

    https://youtu.be/-ecjIrcNAy0

    ReplyDelete

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