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Chapter 9

Chapter 9. Proportions and Similarity. Section 9-1. Using Ratios and Proportions. Ratio. A ratio is a comparison of two numbers by division. Proportion. An equation that shows two equivalent ratios. Cross Products. The cross products in a proportion are equivalent. Means and Extremes.

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Chapter 9

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  1. Chapter 9 Proportions and Similarity

  2. Section 9-1 Using Ratios and Proportions

  3. Ratio • A ratio is a comparison of two numbers by division

  4. Proportion • An equation that shows two equivalent ratios

  5. Cross Products • The cross products in a proportion are equivalent

  6. Means and Extremes In the proportion 20 = 2 30 3 20 and 3 are the extremes and 30 and 2 are the means.

  7. Theorem 9-1 • If a = c, then ad = bc. b d

  8. Section 9-2 Similar Polygons

  9. Similar Polygons • Two polygons are similar if and only if their corresponding angles are congruent and the measures of their corresponding sides are proportional.

  10. Scale Drawing • Used to represent something that is too large or too small to be drawn at actual size.

  11. Scale Factor • The ratio of the lengths of two corresponding sides of two similar polygons

  12. Section 9-3 Similar Triangles

  13. Postulate 9-1 • If two angles of one triangle are congruent to two corresponding angles of another triangle, then the triangles are similar.

  14. Theorem 9-2 • If the measures of the sides of a triangle are proportional to the measures of the corresponding sides of another triangle, then the triangles are similar.

  15. Theorem 9-3 • If the measures of two sides of a triangle are proportional to the measures of two corresponding sides of another triangle and their included angles are congruent, then the triangles are similar.

  16. Section 9-4 Proportional Parts and Triangles

  17. Theorem 9-4 • If a line is parallel to one side of a triangle and intersects the other two sides, then the triangle formed is similar to the original triangle.

  18. Theorem 9-5 • If a line is parallel to one side of a triangle and intersects the other two sides, then it separates the sides into segments of proportional lengths.

  19. Section 9-5 Triangles and Parallel Lines

  20. Theorem 9-6 • If a line intersects two sides of a triangle and separates the sides into corresponding segments of proportional lengths, then the line is parallel to the third side.

  21. Theorem 9-7 • If a segment joins the midpoints of two sides of a triangle, then it is parallel to the third side, and its measure equals one-half the measure of the third side.

  22. Section 9-6 Proportional Parts and Parallel Lines

  23. Theorem 9-8 • If three or more parallel lines intersect two transversals, they divide the transversals proportionally.

  24. Theorem 9-9 • If three or more parallel lines cut off congruent segments on one transversal, then they cut off congruent segments on every transversal.

  25. Section 9-7 Perimeters and Similarity

  26. Theorem 9-10 • If two triangles are similar, then the measures of the corresponding perimeters are proportional to the measures of the corresponding sides.

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