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**Honors Geometry Section 8. 5**

Honors Geometry Section Indirect Measurement & Additional Similarity Theorems

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**Similar triangles can be used to find the height of objects.**

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Proportional Altitudes Theorem If two triangles are similar, then corresponding altitudes are proportional to a pair of corresponding sides.

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**Let’s think about why this theorem is true. Assume , why is ?**

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Proportional Medians Theorem If two triangles are similar, then corresponding medians are proportional to a pair of corresponding sides.

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**Proportional Angle Bisectors Theorem**

Proportional Angle Bisectors Theorem If two triangles are similar, then corresponding angle bisectors are proportional to a pair of corresponding sides.

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**The triangles shown are similar. Solve for x.**

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**The triangles shown are similar. Solve for x.**

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Proportional Segments Theorem An angle bisector of a triangle divides the opposite side into segments which are proportional to the remaining two sides.

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Solve for y.

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