December 18th, 2014, 06:30 PM  #1 
Newbie Joined: Sep 2014 From: USA Posts: 6 Thanks: 0  Similar Triangles Proof
Givens (Attached File) Triangle ABC with AB = AC Altitudes AE and CD 2 problems I'm having trouble with Prove: AF*BE = CF*AD Prove: AC*DB = BE*CB How should I solve this? Should I use transitive property to make several triangles similar? 
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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