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8.5 and 8.6: Proportions in Triangles and Ratios of Perimeters and Areas

8.5 and 8.6: Proportions in Triangles and Ratios of Perimeters and Areas. Objectives: To use the Side-Splitter Theorem to find missing dimensions in triangles To use the Triangle-Angle Bisector Theorem to find missing dimensions in a triangle.

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8.5 and 8.6: Proportions in Triangles and Ratios of Perimeters and Areas

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  1. 8.5 and 8.6: Proportions in Triangles and Ratios of Perimeters and Areas Objectives: To use the Side-Splitter Theorem to find missing dimensions in triangles To use the Triangle-Angle Bisector Theorem to find missing dimensions in a triangle. Find ratios of perimeters and areas of similar figures

  2. Side-Splitter Theorem If a line is parallel to one side of a triangle and intersects the other 2 sides, then it divides those sides proportionally.

  3. Solve for x: 16 10 x 5

  4. Corollary to Side-Splitter Theorem If 3 parallel lines intersect 2 transversals, then the segments intersected on the transversals are proportional

  5. Example: Find x.

  6. Triangle-Angle Bisector Theorem If a ray bisects an angle of a triangle, then it divides the opposite side into 2 segments that are proportional to the other 2 sides of the triangle.

  7. Find the missing length: 1. 2.

  8. Find the value of x. 6 5 8 x

  9. The following triangles are similar. • Find the similarity ratio. • Find the perimeters of both. What is the ratio of the perimeters? • Find the areas of both triangles. What is the ratio of the areas? 10 5 4 8 3 6

  10. Theorem If the similarity ratio of 2 similar figures is a:b, then: • The ratio of their perimeters is a : b • The ratio of their areas is a2: b2 (square the similarity ratio) Remember, always reduce your similarity ratio!!

  11. Two similar polygons have corresponding sides in the ratio 5:7. • Find the ratio of their perimeters. • Find the ratio of their areas.

  12. Find Similarity and Perimeter Ratios The areas of 2 similar triangles are 50 cm2 and 98 cm2. What is the similarity ratio? Ratio of their perimeters? Ratio of areas: Simplify, if possible: Take square root of both sides:

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