Friday, June 22, 2012

Problem 772: Similar triangles with a Common Vertex, Equal Angles, Midpoints, Metric relations

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

Click the figure below to see the complete problem 772.

Online Geometry Problem 772: Similar triangles with a Common Vertex, Equal Angles, Midpoints, Metric relations.

Posted by Antonio Gutierrez at 2:09 PM
Labels: , , , , ,

1 comment:

  1. Peter TranJune 22, 2012 at 4:25 PM

    http://img607.imageshack.us/img607/2298/problem772.png

    Connect lines as shown on the sketch
    We have DE=1/2*BB’ and DF=1/2*CC’
    So DE/DF=BB’/DC
    ∆ABC similar to ∆AB’C’ …( Case AA)
    So AB’/AB=AC’/AC and AB’/AC’=AB/AC=5/6
    ∆AB’B similar to ∆AC’C …. ( case SAS)
    So BB’/CC’=AB’/AC’=5/6
    DE/DF=5/6
    DF=24/5

    ReplyDelete

Subscribe to: Post Comments (Atom)