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Ratios in Similar PolygonsPowerPoint Presentation

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.
- 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

- 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

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

- 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

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