Perimeters and Areas of Similar Figures

1
Section 11-3

• Perimeters and Areas of Similar Figures

2
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.

3
Recall

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

4
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 .

5
If you are given the ratio of the areas, take the
square root of each to find the scale factor or
ratio of perimeters.
6
always, sometimes, or never?

• Two similar quadrilaterals have the same
  perimeter.
• Two squares with the same perimeter are similar.
• Two regular hexagons are similar.

Sometimes
Always
Always
7
always, sometimes, or never?

• Two right triangles with the same area are
  similar.
• Two similar pentagons have the same perimeter.
• Two rectangles with the same area are similar.

Sometimes
Sometimes
Sometimes
8
always, sometimes, or never?

• Two regular decagons are similar.
• Two regular polygons are similar.

Always
Sometimes