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7.2 Using Similar Triangles to Solve Problems

7.2 Using Similar Triangles to Solve Problems. Calvin & Hobbes Math Comics. Solving Problems with Triangles.

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7.2 Using Similar Triangles to Solve Problems

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  1. 7.2 Using Similar Triangles to Solve Problems Calvin & Hobbes Math Comics

  2. Solving Problems with Triangles • Similar triangles can be used to measure the heights of objects that are difficult to get to, such as trees, tall buildings, and cliffs. They can even be used to measure distances across galaxies.

  3. 4 cm 12 cm 5 cm 15 cm 2 cm 6 cm Recall… Consider the following diagram of a pair of similar triangles: How can we tell if two triangles are similar? Once we know that two triangles are similar, we can then use a scale factor, k, to indicate the amount of enlargement or reduction between the triangles.

  4. 4 cm 12 cm 5 cm 15 cm 2 cm 6 cm The Scale Factor The scale factor, k, is the factor that relates corresponding side lengths of two similar triangles. In this example, how much larger is triangle DEF compared to triangle ABC? Hint: What number do we have to multiply each side in triangle ABC by to get the value of the corresponding side in triangle DEF? k = 3

  5. The Scale Factor k = 3 We can represent the scale factor in two ways: OR This means that the side lengths of triangle DEF are three times as large as the corresponding side lengths of triangle ABC. However, we could look at this another way. It also means that the side lengths of triangle ABC are 1/3 the lengths of triangle DEF.

  6. A Final Note… The areas of two similar triangles are related by If , then or . Let’s try some examples!

  7. 3 cm 5 cm 4 cm 3 cm 5 cm 8 cm Example #1: Determine the scale factor, k, for each pair of similar triangles.

  8. 10 cm  15 cm 4 cm   5 cm Example #3: The area of is 8cm2. a) Determine the scale factor. b) Solve for the unknown side lengths. c) Determine the area of .

  9. 20 m water 3 m 4 m Example #2: Given the following diagram, determine the width of the river.

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