Honors Geometry Section 8. 5

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Presentation transcript:

Honors Geometry Section 8. 5 Honors Geometry Section 8.5 Indirect Measurement & Additional Similarity Theorems

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

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

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

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

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.

The triangles shown are similar. Solve for x.

The triangles shown are similar. Solve for x.

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

Solve for y.