SOLUTION: Prove that a line parallel to one side of a triangle divides the other two sides proportionally. Be sure to create and name the appropriate geometric figures.

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Question 1082410: Prove that a line parallel to one side of a triangle divides the other two sides proportionally. Be sure to create and name the appropriate geometric figures.
Answer by Edwin McCravy(20064) About Me  (Show Source):
You can put this solution on YOUR website!

Given: DE∥BC
To prove:  %28DB%29%2F%28AD%29%22%22=%22%22%28EC%29%2F%28AE%29 



ΔADE and ΔAC share ∠A

∠A ≅∠A  reflexive property

DE∥BC is given
∠ADE ≅ ∠B   because they are corresponding angles when transversal
             AB cuts parallel lines DE and BC  
 
ΔADE ∽ ΔABC  a pair of angles in each are congruent

AB%2F%28AD%29%22%22=%22%22%28AC%29%2F%28AE%29  because corresponding sides
                               of similar triangls are proportional

AB%2F%28AD%29-1%22%22=%22%22%28AC%29%2F%28AE%29-1  subtract 1 from each side.

AB%2F%28AD%29-AD%2F%28AD%29%22%22=%22%22%28AC%29%2F%28AE%29-AE%2F%28AE%29 replacing 1's
                    by fractions with equal numrators and dnominators

%28AB-AD%29%2F%28AD%29%22%22=%22%22%28AC-AE%29%2F%28AE%29 Combining fractions.

%28DB%29%2F%28AD%29%22%22=%22%22%28EC%29%2F%28AE%29 Combining fractions.

Edwin