Section 11-3Perimeters and Areas of Similar

Figures

Recall: Two polygons are similar iff

corresponding angles are congruent and the lengths of corresponding sides are proportional.

The ratio of the lengths of two corresponding sides of two similar polygons is called the scale factor.

Recall:

• The ratio of the perimeters of two similar polygons is the same as the scale factor.

Areas of Similar Polygons Theorem

• If two polygons are similar with the lengths of corresponding sides in the ratio , then the ratio of their areas is .

ba :22 :ba

If you are given the ratio of the areas,

take the square root of each to find the scale factor or ratio

of perimeters.

always, sometimes, or never?1.Two similar quadrilaterals

have the same perimeter.

2.Two squares with the same perimeter are similar.

3.Two regular hexagons are similar.

Sometimes

Always

Always

always, sometimes, or never?

4. Two right triangles with the same area are similar.

5. Two similar pentagons have the same perimeter.

6. Two rectangles with the same area are similar.

Sometimes

Sometimes

Sometimes

always, sometimes, or never?

7. Two regular decagons are similar.

8. Two regular polygons are similar.

Always

Sometimes