please help me i will fan and give medal!

Question

bia_gonzalex · Answer

Prove that a line that divides two sides of a triangle proportionally is parallel to the third side. Be sure to create and name the appropriate geometric figures

pyxieyt · Answer

Okay so lets start with a triangle|dw:1448343794253:dw|

pyxieyt · Answer

They say to prove that it is parallel so lets draw a line.|dw:1448343901075:dw|

pyxieyt · Answer

Do you know our goal?

pyxieyt · Answer

@bia_gonzalex

directrix · Answer

The theorem to be proved is the converse of the Triangle Proportionality Theorem.

@bia_gonzalex

pyxieyt · Answer

Do you know the Triangle Proportionality Theorem?

pyxieyt · Answer

The Theorem is if a line parallel to one side of a triangle intersects the other two sides of the triangle, then the line divides these two sides proportionally. Do you see the parallel lines in the triangle above?

pyxieyt · Answer

It's okay can you name the parallel lines? (^o^)

pyxieyt · Answer

|dw:1448344876804:dw| Line DE and BC are parallel!

pyxieyt · Answer

No problem! Now with the theorem is DE=BC then....|dw:1448344963487:dw|

pyxieyt · Answer

Yep, unless they want you to fill in the variables!

pyxieyt · Answer

A good vocabulary word to use would be 'proportionally divides' it is the line that cuts in half!

pyxieyt · Answer

No problem!

directrix · Answer

Here's a YouTube proof of the theorem for review. https://www.youtube.com/watch?v=TwRayRugvAw