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Identifying and Using Similar Polygons through Proportions

In this lesson, students will learn to identify similar polygons by analyzing their corresponding angles and side lengths. They will explore similarity statements, calculate scale factors, and apply the concept of perimeters of similar figures to real-world scenarios. Examples include comparing triangles and finding unknown values in similar polygons. Students will practice writing similarity statements and understanding the relationships between polygons in a hands-on manner. This foundational knowledge will assist in geometry and spatial reasoning skills.

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Identifying and Using Similar Polygons through Proportions

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  1. 6.3 Use Similar Polygons Learning Target: Students will be able to use proportions to identify similar polygons. March 31, 2014

  2. Ex 1: Use Similarity Statements E • Similar Polygons- two polygons are similar if corresponding angles are congruent and corresponding side lengths are proportional In the diagram ΔABC ~ ΔDEF • List all pairs of congruent angles. • Check that the ratios of corresponding side lengths are equal. • Write the ratios of the corresponding side lengths in a statement of proportionality. B 35 28 25 20 C A D F 30 42

  3. Ex 2: Find the Scale Factor • Scale Factor- the ratio of the lengths of two corresponding sides of two polygons Determine whether the polygons are similar. If they are, write a similarity statement and find the scale factor of RSTU and DEFG. 3 : 2 RSTU ~ DEFG S E 30 20 D R 8 12 18 27 U G 22 F 33 T

  4. Ex 3: Use Similar Polygons H B • In the diagram, ΔABC ~ΔGHJ. Find the value of x. 16 8 x 12 J G 12 C A 18

  5. Ex 4: Find Perimeters of Similar Figures • Theorem 6.1- Perimeters of Similar Polygons If two polygons are similar, then the ratio of their perimeters is equal to the ratios of their corresponding side lengths. • You are constructing a rectangular play area. A playground is rectangular with length 25 meters and width 15 meters. The new play area will be similar in shape, but only 10 meters in length. a) Find the scale factor of the new play area to the playground. 10 : 25 or 2 : 5 b) Find the perimeter of the playground and the play area. Playground = 80 meters Play Area -

  6. Ex 5: Use a Scale Factor N • In the diagram, ΔMNP ~ΔRST. Find the length of the altitude NL. • Find the scale. • Find NL. 27 30 M P R T L 20 14 18 S

  7. Guided Practice • In the diagram, ΔJKL ~ΔEFG • Find scale factor. • Find KM. 40 H E G K 35 F J L M 48

  8. Assignment Pg. 376 #4-24 even

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