Anyone good with Geometry? Will medal and fan

Question

anonymous · Answer

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

aihberkhan · Answer

|dw:1452206844256:dw|

aihberkhan · Answer

We are going to use that triangle

anonymous · Answer

So ABC? and then DE divides the triangle?

aihberkhan · Answer

Well, we know that DE is parallel to BC.

Also, the triangles ADDE and ABC are similar. This is because, angle A is shared by both triangle.

AND angle ADE is equal to angle ABC, they are corresponding angles. 

So, by using the two angles postulate, ADE and ABC are similar.

We do:

$AB / AD = AC / AE$

$(AD+DB) / AD = (AE + EC) / AE$

$1 + DB / AD = 1 + EC / AE$

Then, you want to subtract 1:

$DB / AD = EC / AE$

This then proves that a line parallel to one side of a triangle divides the two other sides proportionally.

aihberkhan · Answer

Hope this helped! Have a great day! :)

A medal would also be appreciated! Just click best response next to my name! 

Also, a fan would be appreciated as well! Just hover over my icon and click "Become A Fan". This will allow you to see every time I am online! :) 

If you see that I am online and need help with a question, just tag me in your question! 

@lolbug