Similar Polygons ‐ Lesson: 8.1

8.1SimilarPolygons.notebook

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Similar Polygons ‐ Lesson: 8.1

Bell work: Solve the proportion.

1. 2. 3.

4. 5. 6.

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Triangles and are similar if a similarity transformation preserves angles and reduces or enlarges sides by a scale factor k.

Corresponding angles are congruent

Corresponding sides are proportional


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Ex. 1 ‐ Using Similarity Statements

In the diagram, △RST ∼ △XYZ.

a. Find the scale factor from △RST to △XYZ.

b. List all pairs of congruent angles.

c. Write the ratios of the corresponding side

lengths in a statement of proportionality.

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Corresponding Lengths in Similar Polygons

If two polygons are similar, then the ratio of any two corresponding lengths in the polygons is equal to the scale factor of the similar polygons.


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Ex 2. Solve for x if

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Ex. 3 In the diagram, △TPR ∼ △XPZ.

Find the length of the altitude .


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Ex. 4 Ex. 5

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Theorem 8.1 ‐ Perimeters of Similar Polygons

If two polygons are similar, then the ratio of their perimeters is equal to the ratios of the corresponding sides.


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Ex. 6 ‐ A town plans to build a new swimming pool. An Olympic pool is rectangular with a length of 50 meters and a width of 25 meters. The new pool will be similar in shape to an Olympic pool but will have a length of 40 meters. Find the perimeters of an Olympic pool and the new pool.

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Theorem 8.2 ‐ Areas of Similar Polygons

If two polygons are similar, then the ratio of their areas is equal to the squares of the ratios of their corresponding side lengths.


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Ex. 7 ‐ In the diagram, △ABC ∼ △DEF. Find the area of △DEF.

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Similar Polygons ‐ Lesson: 8.1

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