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Proportional Perimeters & Special Segments of Similar Triangles

Learn about the Proportional Perimeters Theorem, Special Segments of Similar Triangles, and the Angle Bisector Theorem. Discover how corresponding altitudes, angle bisectors, and medians are proportional to corresponding sides in similar triangles. Complete the homework assignments on pages 30 and 31.

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Proportional Perimeters & Special Segments of Similar Triangles

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  1. Chapter 7 Lesson 5: Parts of Similar Triangles Geometry CP Mrs. Mongold

  2. Proportional Perimeters Theorem • If two triangles are similar, then the perimeters are proportional to the measures of corresponding sides. 2 2 SF = ¼ P of small is 6 P of big is 24 6:24 1:4 8 8 2 8

  3. Special Segments of Similar Triangles • Similar Triangles have corresponding altitudes that are proportional to corresponding sides. U Q P R A V W T

  4. Special Segments of Similar Triangles Continued • Similar triangles have corresponding angle bisectors that are proportional to the corresponding sides U Q V R X P T B

  5. Special Segments of Similar Triangles Continued • Similar Triangles have corresponding medians proportional to the corresponding sides. U Q V R Y P T M

  6. Angle Bisector Theorem • An angle bisector in a triangle separates the opposite side into segments that have the same ratio as the other two sides. C B A D

  7. Homework • Pg 30/9 & 10 • Pg 31/7& 8 • Pg 36

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