Lesson 7 2 Similar Polygons Scale Drawings Scale

Lesson 7. 2: Similar Polygons

Scale Drawings • Scale Drawing: A smaller sketch in which all sides are proportional to their actual length. • Proportion: • Ex: A scale model of the Empire State Building is set at 1 in. = 15 m. If the model is 29. 5 in. tall, then what is the height of the Empire State Building?

Practice • A scale model of the Burj Khalifa is set at 1 in. = 35 m. If the model is 23. 66 in. tall, then what is the height of the Burj Khalifa? • A shadow of ARGS extends 10 ft, while my own shadow extends 18 in. If I am 76 inches tall, then what is the height of the school?

Similar Polygons • Similar Polygons: • Scale Factor: The ratio of corresponding sides. (A number each side may be multiplied by to find the corresponding side. )

Practice • ABCD ~ EFGH. What side does AB correspond to? What is the scale factor of AB to EF? What is the value of each variable? 20 F E A 10 B 3 y x 15 D 3 z C H 4 z + 25 40 G

Practice • ABCD ~ EFGH. What side does AB correspond to? What is the scale factor of AB to EF? What is the value of each variable? 30 F E A 20 B 3 y x 15 D 3 z C H 4 z + 25 40 G

Lesson 7. 3: Proving Triangles Similar

Congruency vs. Similarity • Congruency: • Similarity:

Triangle Similarity • Triangle similarity:

Practice • Is △A similar to … If so, why? 2. 25 9 A 12 16 3 4 D B C 4 10 3

Practice • Why isn’t △A ~ △E? 9 12 A 16 6 E 4. 5

Scale Factors in Triangles • Scale factors in Triangles: • Ex: What is the value of x? . D 20 25 12 15 E x F

Practice • ∆ABC ~ ∆DEF. Find the length of EF. C 16 A D 30 20 10 8 B E x F

Practice • What are the values of x and y? A 10 D x 50 B 16 60 C E 2 y – 10 F

Classwork • Lesson 7. 2, #1 – 6 Lesson 7. 3, #1 – 4

Homework • Lesson 7. 2, #13 – 29 odd Lesson 7. 3, #18 – 24 • Lesson 7. 4, #5 – 19 odd Lesson 7. 5, #9 – 29 odd