Similar PolygonsInvestigation 3

Polygon - a closed plane figure, having three or more, usually straight, sides.

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 a rep-tile.

3.2 Rep–Tile TrianglesForming Rep–Tiles w/ Similar Triangles

2 in 2 in 2 in

Original

Rep-Tiled Triangle

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.

Side 1

Side 1

S

ide 2

Rep-Tiled FigureArea = (SF)2 times

the original area

3.3 Scale Factors & Similar Shapes

Two main Criteria for identifying similar figures:• Scale Factor • Angle Measurements

Is ABCD ~ EFGH?

A

D

B

C

2 cm

E

F G

H4 cm

3 cm6 cm

Scale Factor

2 cm x 2 = 4 cm

3 cm x 2 = 6 cm

Yes ABCD ~ EFGH

3.3 Scale Factors & Similar Shapes

Is Δ ABC ~ Δ DEF?

A

B

C

Interior angles of a triangle = 180°

75°40°

X

E

F

75°

75° + 40° + X = 180°

115° + X = 180°

115° + 65° = 180°

65°

Angle Measurements

<A & < D = 65°

<B & <E = 40°

<C & <F = 75°

Yes Δ ABC ~ Δ DEF

D