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bethjewell1996 Group Title

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

  • one year ago
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  1. bethjewell1996 Group Title
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  2. LogicalApple Group Title
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    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.

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  3. LogicalApple Group Title
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    I mean to say, each triangle "share three angles", not that the three angles are all the same, per se.

    • one year ago
  4. bethjewell1996 Group Title
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    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
  5. LogicalApple Group Title
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    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
  6. bethjewell1996 Group Title
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    Okay thank you so much for you help :)

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