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

2. 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. 3.2 Rep–Tile Triangles Forming Rep–Tiles w/ Similar Triangles
Rep-Tiled Triangle
Side 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 Δ ABC ~ Δ DEF
Is Δ ABC ~ Δ DEF? A E D X
65°
75°
40° C B
75°
75° ° + X = 180°
115° X = 180°
115° ° = 180° F
Interior angles of a triangle = 180°