7.5 Parts of Similar Triangles

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Presentation transcript:

7.5 Parts of Similar Triangles Assignment 8: 7.5 WB Pg. 92 #1 – 7 all

Special Segments of Similar Triangles: Theorem 7.8 Similar triangles have corresponding altitudes proportional to the corresponding sides.

Special Segments of Similar Triangles: Theorem 7.9 Similar triangles have corresponding angle bisectors proportional to the corresponding sides.

Special Segments of Similar Triangles: Theorem 7.10 Similar triangles have corresponding medians proportional to the corresponding sides.

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

Example 1 Continued Write the statement of proportionality, be sure to include the altitudes given. Fill in given information and solve

Example 2 Triangle EFD ~ Triangle JKI. EG and JL are medians of their respective triangles. Find JL if EF = 36, EG = 18, and JK = 56.

Theorem 7.11: 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