Ratios in similar polygons
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Ratios in Similar Polygons. Students will be able to apply properties of similar polygons to solve problems. Similarity. Figures that are similar ( ∼ ) have the same shape but not necessarily the same size .

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Ratios in Similar Polygons

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Ratios in similar polygons

Ratios in Similar Polygons

Students will be able to apply properties of similar polygons to solve problems


Similarity

Similarity

  • Figures that are similar (∼) have the same shape but not necessarily the same size.

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

  • A similarity ratio is the ratio of the lengths of the corresponding sides of two similar polygons.

Unit F


Similar figures

Similar Figures

  • When we write a similarity statement, ΔABC ∼ΔLMN for two triangles, we always write each corresponding part in the same order. For example: If, then ∠A corresponds to ∠L, ∠B corresponds to ∠M, and ∠C corresponds to ∠N.

Also, corresponds to ___

corresponds to ___ and

corresponds to ___.

B

M

N

L

A

C

Unit F


Ratios in similar polygons

Example 1: Determining Similarity

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

Step 1: Identify pairs of congruent angles.

M  N, L  P, J  S

Step 2: Compare corresponding sides.

Unit F


Example 2 hobby application

Example 2: Hobby Application

  • Find the length of the model to the nearest tenth of a centimeter.

  • Let x be the length of the model in centimeters.

  • The rectangular model of the racing car is similar to the rectangular racing car, so the corresponding lengths are proportional.

Unit F


Ratios in similar polygons

Example 2 (Continued)

5(6.3) = x(1.8)

31.5 = 1.8x

17.5 = x

The length of the model is.

Unit F


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