section 5-6

Using Similar Figures


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What You'll Learn

  1. To identify similar figures
  2. To find missing lengths in similar figures

… And Why

To measure distances indirectly, as in Example 3

Identifying Similar Figures


Investigation:Exploring Similar Figures

  1. Which pairs of figures have the same shape but not necessarily the same size?
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  2. What is true about the angles of the figures with the same shape?

When two figures have the same shape, but not necessarily the same size, they are similar. In the similar triangles below, corresponding angles have the same measure. Since 40 over 60 = 50 over 75 = 34 over 51, the corresponding sides are proportional. You write ΔABC ~ ΔFGH, where the symbol ~ means "is similar to."

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A polygon is a closed plane figure formed by three or more line segments that do not cross.

Key ConceptsSimilar Polygons

Two polygons are similar if

  • corresponding angles have the same measure, and
  • the lengths of corresponding sides form equal ratios.

Example 1 Verifying That Figures Are Similar

Verify that the triangles are similar.

detail via d link.dThe measures of angleX and angleP are 76.5°. The measures of angleY and angleQ are 41.5°. The measures of angleZ and angleR are 62°. 40 over 80 = one over two, 44 over 88 = one over two, and 30 over 60 = one over two.

The measures of corresponding angles are equal. The lengths of corresponding sides form equal ratios. So the triangles are similar.

Interactivity icon Interactivity Similar polygons

Course 2 iText


Chapter 5
Ratios, Rates, and Proportions