Circle Limit III M.C. Escher Section 6-2 Spi.2.2.B Jim Smith JCHS JCHS

Similar figures look alike but one is a smaller version of the other. Like Dr. Evil and Mini-Me. version of the other. Like Dr. Evil and Mini-Me. It wouldn’t make much sense to make a drawing It wouldn’t make much sense to make a drawing of this ship the actual size of the ship.

Just like congruent polygons, the corresponding angles in similar polygons must be congruent.

AX C D B W Z Y A = 80° B = 30° Z = 170° A = 80° B = 30° Z = 170° W = ___ X = ___ D = ___ W = ___ X = ___ D = ___ 80°30°170°

The sides are a little different. They must be PROPORTIONAL. A X C D B W Z Y AB = BC = CD = DA AB = BC = CD = DA WX XY YZ ZW WX XY YZ ZW

This means I should be able to multiply each side of the smaller polygon by the same number and get it’s corresponding side on the bigger polygon. 4 4x2 = 8 5 5x2 = x2 = 4 3 3x2 = 6

The SCALE FACTOR is the ratio of the corresponding sides of the corresponding sides SMALL BIG BIG SMALL BIG SMALL or

What is the scale factor of these polygons? 10 4 X7 Y 8 Z 6 Scale Factor = 104 = 52

4 7 Y Z 10 X =52 Use the scale factor to find the other sides Z = 5z = 12 z = 12 = 2.4 z = 12 = SF = 5 X 2 7 2x = 35 x = 35 = 17.5 x = 35 = = Y 5y = 16 y = 16 = 3.2 y = 16 = =