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Section 8.3 Similar polygons

Learn how to identify, apply, and calculate similarity in polygons through ratios, proportions, and scale drawings. Discover the importance of congruent angles and corresponding side lengths. Practice precision in mathematical understanding.

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Section 8.3 Similar polygons

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  1. Section 8.3Similar polygons OBJECTIVE: To identify and apply similar polygons BIG IDEA: Proportionality ESSENTIAL UNDERSTANDINGS; Ratios and proportions can be used to decide whether two polygons are similar and to find unknown lengths of similar figures. All lengths in a scale drawing are proportional to their corresponding actual lengths. MATHEMATICAL PRACTICE: Attend to precision

  2. SIMILAR POLYGONS • Two polygons are SIMILAR POLYGONS if their ________________________ angles are __________________ and if the lengths of corresponding _______________ are ________________________. The symbol for “is similar to” is __________. You write a similarity statement with corresponding vertices in order, just as you write a congruence statement.

  3. Understanding similarity • A) What are the pairs of congruent angles? • B) What is the extended proportion for the ratios of the corresponding sides in a statement of proportionality.

  4. EX 1: Are the polygons similar? • Write the similarity statement.

  5. Similar polygons • SCALE FACTOR: the ratio of ____________________ linear measurements of two _______________ figures. • SCALE DRAWING: a drawing in which all lengths are ____________________ to corresponding _______________ lengths. A scale is the _______________ of any length in a scale drawing to the corresponding actual length. • THM 8.1: If two polygons are _______________, then the _______________ of their ____________________ is equal to the _______________ of their corresponding side _______________

  6. Ex 2: in the diagram, • A) List all pairs of congruent angles and write the statement of proportionality for the polygons. • B) Find the scale factor of TUVW to ABCD

  7. Ex 2: in the diagram, • C) Find the length of • D) Find the measure of

  8. Ex 3: pentagon abcde is similar to pentagon jklmn • Write the scale factor and find the value of x.

  9. Ex 4: • What are the values of x and y?

  10. Ex 5: using a scale drawing • You have a scale drawing of the Golden Gate Bridge in San Francisco with a scale of 1 cm = 200 m. The distance between the two towers is the main span. The length of the main span in the scale drawing is 6.4 cm. What is the actual length of the main span of the bridge?

  11. 25 questions 8.3 p. 4768 – 10 all, 12 – 18 evens, 19- 28 all, 30, 40, 42, 46, 54 – 66x3

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