Geometry Problem

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

Click the figure below to see the complete problem 772.

## Friday, June 22, 2012

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

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

ReplyDeleteConnect 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