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December 18th, 2014, 06:30 PM   #1
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Similar Triangles Proof

Givens (Attached File)
Triangle ABC with AB = AC
Altitudes AE and CD

2 problems I'm having trouble with

Prove: AC*DB = BE*CB

How should I solve this? Should I use transitive property to make several triangles similar?
Attached Images
 Triangle.jpg (6.7 KB, 11 views)

 December 19th, 2014, 08:40 AM #2 Global Moderator     Joined: Oct 2008 From: London, Ontario, Canada - The Forest City Posts: 7,923 Thanks: 1123 Math Focus: Elementary mathematics and beyond $\displaystyle \triangle{ADF}\sim\triangle{CEF}\implies\frac{CE}{ AD}=\frac{CF}{AF}\implies\frac{BE}{AD}=\frac{CF}{A F}\implies AF\cdot BE=CF\cdot AD$ $\displaystyle \triangle{AEC}\sim\triangle{CDB}\implies\frac{AC}{ CE}=\frac{CB}{DB}\implies AC\cdot DB=CE\cdot CB\implies AC\cdot DB=BE\cdot CB$

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