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Published byLuke Whinnery Modified over 2 years ago

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Honors Geometry Section 8.5 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 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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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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