1. Similar Polygons Learning Target: I can use ratios and proportions to determine if two polygons are similar and to find unknown side lengths.

2. Properties of Similarity Two polygons are similar if 1. corresponding angles are congruent 2. corresponding sides are proportional The symbol for similarity is ~

3. ABCD~EFGH. 1. m<E=____ 2. AB = AD EF __ Are corresponding angles ≅ ? Are corresponding sides proportional? B A C D F E G H 53 127 m<A EH yes

4. Similar Ratio - the ratio of the lengths of corresponding sides A B C D E F 15 18 12 20 16 24 Are the corresponding sides proportional? AB/FE=15/20=.75 BC/ED=12/16=.75 AC/FD=18/24=.75 yes

5. The polygons are similar. Find the value of the variables. 1. 2. 3. 4. 6 5 x 3.3 5 3 8 x x 10 1.5 4 x 15 6 9 x=2.75 x=4.8 x=3.75 x=10

6. 10 B A C 14 12 Are the polygons similar? If they are, write a similarity statement, and give the similarity ratio. 6 5 7 X Z Y AB/XY=10/5=2 AC/XZ=12/6=2 BC/YZ=14/7=2 Triangle ABC~XYZ with similarity ratio 2:1