Similar Polygons Circle Limit III M.C. Escher
Figures that are similar (~) have the same shape but not necessarily the same size.
Similar figures look alike but one is a smaller version of the other. It wouldn’t make much sense to make a drawing of this ship the actual size of the ship.
All the angles are the same All sides are proportional Two polygons are similar polygons if and only if their corresponding angles are congruent & their corresponding side lengths are proportional. All the angles are the same All sides are proportional
Similar Polygons – 2 polygons that have the same shape but not the same size. Symbol ( ~ ) Corresponding s are . Corresponding sides are Proportional. Equal Ratios: ** Reduce to the same fraction!!
Writing a similarity statement is like writing a congruence statement—be sure to list corresponding vertices in the same order. Writing Math
Ex: Order Matters ΔABC ~ ΔXYZ 4 6 = AB = 15 10 AB 4 8 = AC = 20 10 AC 78 4 6 BC corresponds to YZ B 42 Z X 8 10 Find AB: 4 6 = AB = 15 10 AB A C 4 8 = mB = mC = 78 60 AC = 20 Find AC: 10 AC
Example : Identifying Similar Polygons Determine whether the polygons are similar. If so, write the similarity ratio and a similarity statement. rectangles ABCD and EFGH
Example 3 A boxcar has the dimensions shown. A model of the boxcar is 1.25 in. wide. Find the length of the model to the nearest inch.
Example 3 Continued 1.25(36.25) = x(9) Cross Products Prop. 45.3 = 9x Simplify. 5 x Divide both sides by 9. The length of the model is approximately 5 inches.
Ex. 2: Are the following polygons similar? B C 120 1in K L 1in 4in 4in 2in 2in 80 J M 1in A D 2in Check to see if all s are ? Check the ratio of all corresponding sides?