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Parts of Similar Triangles

Parts of Similar Triangles. Section 7.5. Proportional Perimeters Theorem. If two triangles are similar, then the perimeters are proportional to the measures of the corresponding sides. Example 1:

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Parts of Similar Triangles

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  1. Parts of Similar Triangles Section 7.5

  2. Proportional Perimeters Theorem • If two triangles are similar, then the perimeters are proportional to the measures of the corresponding sides.

  3. Example 1: • Write the statement of proportionality • to find the scale factor • Scale factor = 2/3

  4. Find the perimeter of one triangle. • Triangle ABC P = • Set up a proportion with the scale factor and the perimeter.

  5. Solve the proportion

  6. Special Segments of Similar Triangles • Similar triangles have corresponding altitudes proportional to the corresponding sides.

  7. Similar triangles have corresponding angle bisectors proportional to the corresponding sides.

  8. Similar triangles have corresponding medians proportional to the corresponding sides.

  9. Examples • 1. Triangle JLM ~ triangle QST. KM and RT are altitudes of the respective triangles. Find RT if JL = 12, QS = 8, and KM = 5

  10. Write the statement of proportionality, be sure to include the altitudes given. • Fill in given information and solve

  11. Triangle EFD ~ Triangle JKI. EG and JL are medians of their respective triangles. Find JL if EF = 36, EG = 18, and JK = 56.

  12. 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

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