Honors Geometry Section 8.5 Indirect Measurement & Additional Similarity Theorems - PowerPoint PPT Presentation

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Honors Geometry Section 8.5 Indirect Measurement & Additional Similarity Theorems

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Honors Geometry Section 8.5 Indirect Measurement & Additional Similarity Theorems

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  1. Honors Geometry Section 8.5Indirect Measurement & Additional Similarity Theorems

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

  3. Proportional Altitudes TheoremIf two triangles are similar, thencorresponding altitudes are proportional to a pair of corresponding sides.

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

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

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

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

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

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

  10. Solve for y.