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6.3: Ratio Use Similar Polygons

6.3: Ratio Use Similar Polygons. Objectives: Identify Similar Polygons Apply Properties of Similar Polygons to Solve Problems. Common Core Objectives: G-SRT-2, G-SRT-5 Assessments Define all vocab for this section Do worksheet 6-3.

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6.3: Ratio Use Similar Polygons

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  1. 6.3: Ratio Use Similar Polygons Objectives: Identify Similar Polygons Apply Properties of Similar Polygons to Solve Problems. Common Core Objectives: G-SRT-2, G-SRT-5 Assessments Define all vocab for this section Do worksheet 6-3

  2. Figures that are similar(~) have the same shape but not necessarily the same size.

  3. Determine whether the polygons are similar. If so, write the similarity ratio and a similarity statement. rectangles ABCD and EFGH

  4. Thus the similarity ratio is , and rect. ABCD ~ rect. EFGH. Step 1 Identify pairs of congruent angles. A  E, B  F, C  G, and D  H. All s of a rect. are rt. s and are . Step 2 Compare corresponding sides.

  5. Two polygons are similar polygons if and only if their corresponding angles are congruent and their corresponding side lengths are proportional.

  6. Identify the pairs of congruent angles and corresponding sides. Check that the ratios of corresponding side lengths are equal. Write the ratios of the corresponding side lengths in a statement of proportionality. 0.5

  7. Determine whether the polygons are similar. If they are, write a similarity statement and find the scale factor of ZYXWto FGHJ. EXAMPLE 2

  8. Determine if ∆JLM ~∆NPS. If so, write the similarity ratio and a similarity statement.

  9. Perimeters of similar polygons: If two polygons are similar the ratio of the perimeters will be the same as the ratio of their corresponding side lengths.

  10. A town is building a new swimming pool. An Olympic pool is rectangular with length 50 meters and width 25 meters. The new pool will be similar in shape, but only 40 meters long.2 b. Find the perimeter of an Olympic pool and the new pool. a. Find the scale factor of the new pool to an Olympic pool. EXAMPLE 4

  11. In the diagram, ∆TPR~∆XPZ. Find the length of the altitude PS. EXAMPLE 5 First, find the scale factor of ∆TPRto ∆XPZ. Then apply it to the altitude.

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