Ch 4 4 Similar Figures and Proportions Similar

Ch. 4 -4 Similar Figures and Proportions Similar Not Similar Similar

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

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

Ch. 4 -4 Similar Figures and Proportions. -If two polygons are similar polygons, then *corresponding angles are congruent Equal *lengths of corresponding sides are in proportion Example of two similar polygons: 15 7. 5 12 Big 6 Small -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! 4 Big 10 Small 3 -Corresponding Angles are congruent But do the sides form a proportion? 8 30 doesn’t = 32, not similar 1000 Have to check 2 things! 1000 -Corresponding Angles are congruent But do the sides form a proportion? 9 6 Small Big 24 = 22. 5, not similar figures 400 4 400 2. 5 400

Example 2: Use what you know about similar figures to solve for the unknown measurements. 16 x Need to set up a proportion: 9 18 Small Big Now cross multiply and divide: (18 * 16) / 9 = x x = 32 Need to set up a proportion: Small 10 Now cross multiply and divide: x Big (10 * 2) / 4 = x 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 21 Need to set up a proportion: 24 y Now cross multiply and divide: 42 (42 * 24) / 21 = y 21 Big Small 24 y y = 48

30 30 Big y 90 30 60 y Small 60 Need to set up a proportion: Now cross multiply and divide: (60 * 30) / 90 = y y = 20

Homework Page 183 #6 -18 even (#14 e. c. ) # 8 -14 show proportions