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Similar Polygons Investigation 3

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.

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Similar Polygons Investigation 3

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

  2. 3.1 Rep-Tile QuadrilateralsForming 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 arep-tile.

  3. 3.2 Rep–Tile TrianglesForming 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

  4. 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

  5. 3.3 Scale Factors & Similar Shapes Angle Measurements <A & < D = 65° <B & <E = 40° <C & <F = 75° Yes ΔABC ~ ΔDEF Is ΔABC ~ ΔDEF? 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°

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