Geometry 6.3Geometry 6.3

Big Idea: Use Big Idea: Use Similar PolygonsSimilar Polygons

Similar PolygonsSimilar Polygons: : Two Two polygons where polygons where corresponding corresponding angles are angles are congruentcongruent and and corresponding corresponding side side lengths are proportionallengths are proportional (not congruent)(not congruent)

Symbol for similarity isSymbol for similarity is ~~

Scale FactorScale Factor: : In two similar In two similar polygons, the polygons, the ratioratio of the of the lengths of two lengths of two corresponding sides. All corresponding sides. All corresponding sides have corresponding sides have the the same ratiosame ratio for similar for similar polygons.polygons.

Theorem 6.1 Perimeters of Similar Polygons

If two polygons are similar, then the ratio of their perimeters is equal to the ratios of their corresponding sides

(scale factor).

Example: In the diagram,1) List all pairs of congruent

angles.

2) Check that the ratios of corresponding sides lengths are equal.

3) Write ratios of the corresponding side lengths in a statement of proportionality.

1) What is the scale factor?

2) What is the ratio of the perimeters?

1. Are these triangles similar?

1. If yes, what is the scale factor?

2. What is the ratio of the perimeters?

Example: In the diagram,

Find the value of x.

In the diagram,

1. Find the value of x.

2. What is the scale factor of QRST to ABCD?