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

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

Examples of Polygons

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.

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

Example 1: Identify Similar Polygons 3 4.2 M H L E 1.1 1.5 1.54 2.1 A O 3.5 T 4.9 V Compare corresponding angles: Compare corresponding sides: 𝐿𝑂 𝑀𝐴 = 1.54 1.1 =1.4 𝑂𝑉 𝐴𝑇 = 4.9 3.5 =1.4 𝐸𝑉 𝐻𝑇 = 2.1 1.5 =1.4 𝐿𝐸 𝑀𝐻 = 4.2 3 =1.4 ∠𝑀=90° 𝑎𝑛𝑑 ∠𝐿=90° ∠𝐴=100° 𝑎𝑛𝑑∠𝑂=100° ∠𝑇=80° 𝑎𝑛𝑑∠𝑉=80° ∠𝐻=90° 𝑎𝑛𝑑∠𝐸=90° 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.

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

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 𝐾𝐿 𝑄𝑅 = 𝐿𝑀 𝑅𝑆 32 5 = 𝑥 9 𝑥=57.6 The missing side length is 57.6cm.

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

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