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Identifying and Using Similar Polygons in Geometry

Explore the concept of similar polygons, focusing on identifying congruent angles and proportional sides. Learn how to use similarity statements, such as trapezoids and parallelograms, with real-life examples like reducing photo sizes to fit frames. Work through various exercises, including calculating scale factors and verifying the similarity of different geometric shapes. Engage with practical applications, such as comparing paintings to walls, and understand how to apply geometric principles effectively.

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Identifying and Using Similar Polygons in Geometry

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  1. 8.3 Similar Polygons IDENTIFYING SIMILAR POLYGONS 1 GOAL EXAMPLE 1 • VOCABULARY • similar polygons • scale factor

  2. B C Q R P S A D Extra Example 1 Trapezoid ABCD is similar to trapezoid PQRS. List all the pairs of congruent angles, and write the ratios of the corresponding sides in a statement of proportionality.

  3. Extra Example 2 Decide whether the figures are similar. If they are, write the similarity statement.

  4. 6 in x 1.5 in 4 in Extra Example 3 You have a photo 4 in. wide by 6 in. long that you want to reduce to fit in a frame that is 1.5 in. wide. How long will the reduced photo be?

  5. Extra Example 4 A painting is similar to the wall on which it is hanging. Calculate the scale factor of the wall to the painting and find the ratio of their perimeters.

  6. 6 1.5 Checkpoint Verify that these two pentagons are similar. Then find the ratio of their perimeters.

  7. 8.3 Similar Polygons USING SIMILAR POLYGONS IN REAL LIFE 2 GOAL

  8. y C D 12 E F 24 15 B G A Extra Example 5 Parallelogram ABCD is similar to parallelogram GBEF. Find the value of y.

  9. Checkpoint ΔUVW is similar to ΔYXW. Find the value of a.

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