Bellringer a.) Sheryl bought 3 pieces of candy for $1.29. At that rate, what would 8 pieces of candy cost her? $3.44

Go over Practice Sheets 5-3 & 5-4 all

Ch. 5-5 Similar Figures and Proportions

have the same shape, but not necessarily the same size Similar Figures have the same shape, but not necessarily the same size Not Similar Similar Similar

Congruent angles have equal measures. All these angles are 90 degrees therefore they are congruent angles 1000 400 400

Ch. 5-5 Similar Figures and Proportions -If two polygons are similar polygons, then *corresponding angles are congruent *lengths of corresponding sides are in proportion Example of two similar polygons: 6 12 7.5 15 -Corresponding angles are congruent and the sides form a proportion! 90 = 90

Example 1: Are the following shapes similar. Explain why or why not. Have to check 2 things! -Corresponding Angles are congruent 4 3 But do the sides form a proportion? 8 10 30 doesn’t = 32, not similar 1000 Have to check 2 things! -Corresponding Angles are congruent 1000 But do the sides form a proportion? 9 6 4 2.5 400 400 400 400 24 = 22.5, NOT similar figures

Need to set up a proportion: Example 2: Use what you know about similar figures to solve for the unknown measurements. 16 Need to set up a proportion: 9 x 18 Now cross multiply and divide: x = 32 Need to set up a proportion: 10 x Now cross multiply and divide: x = 5 2 4

Example 3: The figures below are similar. Find the unknown measurements. You may need to break the figure apart and redraw. 21 Need to set up a proportion: 21 24 y Now cross multiply and divide: y = 48 Need to set up a proportion: 30 y Now cross multiply and divide: y = 20 30 60

Ch. 5-6 Maps and Scale Drawings -a scale model is a model similar to the actual object it represents. -the scale of a models is the ratio of the length of the model to the corresponding length of the actual object. Example 1: Use proportions to solve the following problems. a.) The scale of a map is 1 in. : 10 mi. How many actual miles does 4.4 in. represent? b.) The scale of a map is 1 in. : 4 mi. How many inches does 86 miles represent? x = 44 miles x = 21.5 inches

-indirect measurement uses proportions and similar triangles to measure distances that would be difficult to measure directly. Example 2: A student is 5 ft. tall and casts a 15 ft. shadow. A nearby tree casts a shadow 75 ft. long. Find the height of the tree. x = 25 ft. tall Example 3: A school 40 ft. high casts a 160 ft. shadow. A nearby cellular phone tower casts a 210 ft. shadow. Find the height of the tower. x = 52.5 ft. tall

Homework Page 254 6-10 all, 14-16 e Page 262 6-10 e show proportion show answer

Go over Homework Page 254 6-10 all, 14-16 e Page 262 6-10 e

Practice Sheet 5-6 #1-12 all Show proportions and answers Homework due tuesday Practice Sheet 5-5 all show proportions and answers #12 & #13 show triangles Practice Sheet 5-6 #1-12 all Show proportions and answers

Practice Sheet 5-6 #1-12 all Show proportions and answers Skip #4 Go over Homework Practice Sheet 5-5 all show proportions and answers #12 & #13 show triangles Practice Sheet 5-6 #1-12 all Show proportions and answers Skip #4

Homework Review Problems Page 268 #1-28 all

Go Homework Review Problems Test tomorrow (Thursday) Page 268 #1-28 all Notes due pages 92-108 Test tomorrow (Thursday)