Similar Polygons

1. Similar Polygons

2. Vocabulary • Polygon: Consists of a sequence of consecutive line segments in a plane, placed and to end to form a simple closed figure. • Similar Polygons: Polygons that have the same shape but not necessarily the same size • Corresponding Parts: Parts of similar figures that “match”.

3. Corresponding Angles are congruent • Corresponding side measurements are proportional. • Scale Factor: The ratio of the lengths of two corresponding sides of two similar polygons. • The ratio of the measures of a pair of corresponding sides is the scale factor • The perimeters have a ratio that equals the scale factor. • The areas have a ratio that equals the square of the scale factor.

4. Key Concept WORDS: If two polygons are similar, then • Their corresponding angles are CONGRUENT, or have the same measurement. • The measures of their corresponding sides are proportional MODEL B Y A C Z X SYMBOLS:

5. H J M N 3 6 • Determine whether rectangle HJKL is similar to rectangle MNPQ. Explain K P Q L 10 7

6. A W 24 B X 13 12 m D Given that polygon WXYZ ~ polygon ABCD, find the missing measurement. C 10 Z Y 15

7. Using Scale Factor to Write and Equation A length on polygon WXYZ is 3/2 times as long as …. corresponding length on polygon ABCD Let m represent the measure of XY m = 3/2 · 12

8. Find the missing measure • WZ • AB • Given rectangle LMNO ~ rectangle GHIJ, find the missing measure. L M G H 2 3 I J O N 4 m

9. Ratios of Similar Figures WORDS: If two figures are similar with a scale factor of a/b, then the perimeters of the figures have a ratio of a/b MODEL: a b Figure A Figure B

10. L P 18 24 Triangle LMN is similar to triangle PQR. If the perimeter of ∆ LMN is 64 units, what is the perimeter of ∆ PQR? N R Q M • 108 units • 96 units • 48 units • 36 units

11. Rectangle KLMN is similar to rectangle TUVW. If the perimeter of rectangle KLMN is 32 units, what is the perimeter of rectangle TUVW? • 128 units • 96 units • 64 units • 40 units