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Understanding Similar Polygons in Geometry

Learn to identify, draw, and explain similar polygons using scale factors. Discover how corresponding angles and side lengths are key properties in determining similarity. Includes examples and practice problems.

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Understanding Similar Polygons in Geometry

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  1. Chapter 4 – Scale Factors and Similarity Key Terms • Polygon – a two-dimensional closed figure made of three or more line segments

  2. 4.4 Similar Polygons Learning Outcome: To be able to identify, draw, and explain similar polygons and solve problems using the properties of similar polygons

  3. Examples of Polygons

  4. Similar Polygons • Similar polygons which have been multiplied by a scale factor show an enlargement or reduction. Therefore, similar polygons have: • Corresponding Angles - Equal internal angles • Corresponding Side Lengths - Proportional side lengths (because of scale factor) • But unlike Similar Triangles BOTH need to be true for the polygons to be similar.

  5. Example 1: Identify Similar Polygons The two quadrilaterals look similar. Is LOVE a true enlargement of MATH? Explain. 4.2 3 L M H E 1.1 1.5 1.54 2.1 A O 3.5 T 4.9 V

  6. Example 1: Identify Similar Polygons 4.2 3 L M H E 1.1 1.5 1.54 2.1 A O 3.5 T 4.9 V Compare corresponding sides: Compare corresponding angles: Note: The sum of the interior angles in a quadrilateral is 360 The corresponding angles are equal and the corresponding side lengths are proportional with a scale factor of 1.4. Therefore LOVE is a true enlargement of MATH by a scale factor of 1.4.

  7. Example 2: Determine a Missing Side Length K J Q P 5cm R 9cm S 32cm L M

  8. Example 2: Determine a Missing Side Length K J Q P 5cm R 9cm S 32cm Since the rectangles are similar; the side lengths are proportional. Use corresponding sides to set up a proportion. L M The missing side length is 57.6cm.

  9. Show you Know – The two trapezoids shown are similar. Determine the missing side length. Show your work

  10. Assignment • Page 157 (1, 3, 5-6, 9, 11)

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