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In the figure, the horizontal lines are parallel, and AB = BC = CD. Find KL and FG.
 one year ago
 one year ago
In the figure, the horizontal lines are parallel, and AB = BC = CD. Find KL and FG.
 one year ago
 one year ago

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LogicalAppleBest ResponseYou've already chosen the best response.1
You can see that all the shaded triangles are similar because they all share an angle through parallel lines cut by a transverse line. They are all similar because they each have three equal angles. All three have a 90 degree angle, all three have the same angle between the diagonal and the vertical blue lines, and all three have the same angle between the diagonal and the horizontal parallel lines. To prove that all three triangles are equal, just notice that the diagonal of each triangle is the same since it is given in the question. Since similar sides of similar triangles are equal, the remaining sides must also be equal, and hence the triangles are all congruent. Knowing this, you can already determine EF = FG = GH = 8.8 Use this knowledge, and Pythagorean's theorem, to determine KL.
 one year ago

LogicalAppleBest ResponseYou've already chosen the best response.1
I mean to say, each triangle "share three angles", not that the three angles are all the same, per se.
 one year ago

bethjewell1996Best ResponseYou've already chosen the best response.0
KL = 8.8; FG = 8.8 KL = 8.8; FG = 8.9 KL = 8.9; FG = 8.9 KL = 8.9; FG = 8.8 These are my answers
 one year ago

LogicalAppleBest ResponseYou've already chosen the best response.1
Now that I am looking at the picture, I am assuming KL is the length of the diagonal? In that case it is just another instance of congruent triangles. So KL = 8.9 and FG = 8.8.
 one year ago

bethjewell1996Best ResponseYou've already chosen the best response.0
Okay thank you so much for you help :)
 one year ago
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