Thread: parallel lines and transversals

Lines l1 and l2 intersect each other and 3 parallel lines, l3, l4, and l5, at the points shown below. The ratio of the perimeter of triangle ABC to the perimeter of triangle AFG is 1:3. The ratio of DE to FG is 2:3. What is the ratio of AC to CE?

I know that answer is 1:1 but I'm not sure how to prove it..

"I'm not sure how to prove it.." You're not sure or you don't know?

Indication: Use The Fundamental Theorem of Similarity and/ or Thales' Theorem.

So I looked both of those up and it's still unclear how to use them for this proof.. so how do you prove it?

"So I looked both of those up and it's still unclear how to use them for this proof" ... in ten minutes, well, yeah, obviously it's unclear.

What exactly don't you understand?

I don't understand how to show the result that those lengths are 1:1, so how do you do it??

"Indication: Use The Fundamental Theorem of Similarity and/ or Thales' Theorem." Remember that?

"The ratio of the perimeter of triangle ABC to the perimeter of triangle AFG is 1:3. The ratio of DE to FG is 2:3." This is what you know, use it and The Fundamental Theorem of Similarity for two conveniently chosen triangles. After that thinghs should be clear.

Yeah I know about similarity, what I don't know is how to relate it to this problem? Anyone else wanna help take a crack at this?

Sooo... you're waiting for someone to solve your problem and refuse to think, nice, very nice -_-

"how to relate it to this problem" You sure know that theorems?

"Lines l1 and l2 intersect each other and 3 parallel lines, l3, l4, and l5, at the points shown below."

Simply restating the problem isn't helping and just because I don't see what to do, doesn't mean I'm not thinking about it. So is there anyone who does?

Hi Sarahh.
Draw a triangle ABC with a base BC Mark the midpoints of AB and AC m and n. Draw a line mn. Measure the perimeters of the two triangles . Compare all ratios of the sides of both triangles. Then repeat the procedure with your diagram but with the given perimeters or other info


bjh