How Can the Similarity Theorem Prove Segment Proportions in Triangle ABC?

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In triangle ABC, with D as the midpoint of AB, a line is drawn from D intersecting AC at H and BC at O. The goal is to prove that the segment ratios AH:HC and BO:OC are equal. The similarity theorem states that if a line is drawn parallel to one side of a triangle, it divides the other two sides proportionally. By drawing a line through D parallel to AC, the proportionality can be established. This approach effectively demonstrates the segment proportions in triangle ABC.
Misr
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Hi ,there

ABC is a triangle , D is the midpoint of AB , from D draw a st. line to intersect AC at H and BC at O.
Prove that :

AH : HC = BO: OC
http://img299.imageshack.us/img299/5752/similarity.jpg
We need to solve this problem using the similarity theorem "If a line is drawn parallel to one side of a triangle and intersects the other two sides , then it divides them into segments whose lengths are proportional ".

Thanks in advance
 
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Hint: Draw a line through D which is parallel to AC.

ehild
 
Its very easy right now
Thanks
 

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