The two-column proof with missing statements and reasons proves that if a line parallel to one side of a triangle also intersects the other two sides, the line divides the sides proportionally.

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anonymous · Answer

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anonymous · Answer

You know your final statement is the proposition to be proved.

anonymous · Answer

#5 claims AA similarity and #4 gives one of the angles, so #3 must be for the other angle.

anonymous · Answer

And that other pair of angles being congruent should follow from the situation of parallel lines cut by a transversal.

anonymous · Answer

Yes! I totally forgot the last part is the proven

anonymous · Answer

I'm sorry though, I'm still lost about 3.. I'm better with these questions if they give us possible statements and reasons.

anonymous · Answer

Bah, having multiple choice answers to guess from weakens your critical thinking skills.
Try to recall all the theorems you know that relate to this situation.

anonymous · Answer

You know you need angle-angle similarity, so need one more pair of congruent angles.
There are two pairs to choose from since you have those parallel lines cut by a transversal.

anonymous · Answer

I'm just so bad at proofs, I get so brain dead and can't think of any. :( I was just reviewing this with my teacher and still sucked.

anonymous · Answer

Don't think of it as being good or bad at proofs, just look at the individual situation: parallel lines cut by a transversal, what are all the congruence relations you know for that situation?

anonymous · Answer

Hm. Well Reason 6 is Converse of the Side-Side-Side Similarity Theorem right?

anonymous · Answer

I don't think it's the converse of SSS.
You're trying to prove that the sides are proportional, and the penultimate statement claims similarity.

anonymous · Answer

Wait would statement 3 be angle CAB = angle EDB?

anonymous · Answer

And then that's because they're corresponding

anonymous · Answer

Yes, exactly!

anonymous · Answer

YESS!

anonymous · Answer

okay okay reason 6.. um is it because like corresponding angles in similar triangles are then equal? like the ratio?

anonymous · Answer

Similar figures are proportional.

anonymous · Answer

so reason 6.. similar figures are proportional?

anonymous · Answer

There's probably a more technical way to say that, but that's how I remember that particular theorem.

anonymous · Answer

sounds great though. thank you so much!!

anonymous · Answer

For more info, see Euclid. http://aleph0.clarku.edu/~djoyce/java/elements/bookVI/bookVI.html http://aleph0.clarku.edu/~djoyce/java/elements/bookVI/defVI1.html