Similar Polygons Investigation 3 Polygon - a closed plane figure, having three or more, usually straight, sides.

3.1 Rep-Tile Quadrilaterals Forming Rep–Tiles w/ Similar Quadrilaterals If congruent copies of a shape can be put together to make a larger, similar shape, the original is called a rep-tile.

3.2 Rep–Tile Triangles Forming Rep–Tiles w/ Similar Triangles Rep-Tiled Triangle Side 1 Side 2 Original Side 1 2 in 2 in 2 in Rep-Tiled Triangle Scale Factor = 2 because the side length is 2 times the original. Perimeter = 2 times the perimeter of the original. Area = 4 times the original area because 4 triangles fit into the rep-tiled triangle. Rep-Tiled Figure Area = (SF)2 times the original area

3.3 Scale Factors & Similar Shapes Two main Criteria for identifying similar figures: Scale Factor Angle Measurements Scale Factor 2 cm x 2 = 4 cm 3 cm x 2 = 6 cm Yes ABCD ~ EFGH Is ABCD ~ EFGH? F G A B 2 cm D C 6 cm 3 cm E H 4 cm

3.3 Scale Factors & Similar Shapes Angle Measurements <A & < D = 65° <B & <E = 40° <C & <F = 75° Yes Δ ABC ~ Δ DEF Is Δ ABC ~ Δ DEF? A E D X 65° 75° 40° C B 75° 75° + 40° + X = 180° 115° + X = 180° 115° + 65° = 180° F Interior angles of a triangle = 180°