1. Section 8.3:
Similar Polygons

2. Similar polygons – when there is a correspondence between two polygons such that their corresponding angles are congruent and the lengths of the corresponding sides are proportional. The symbol ~ is used to indicate similarity.

3. In the diagram, ABCD is similar to EFGH.
ABCD ~ EFGH ~ G F H E

4. Example 1: Trapezoid ABCD is similar to trapezoid PQRS
Example 1: Trapezoid ABCD is similar to trapezoid PQRS. List all the pairs of congruent angles, and write the ratios of the corresponding sides in a statement of proportionality. B C Q R P S A D

5. Angles: Sides: ~

6. Example 2: Determine whether the figures are similar
Example 2: Determine whether the figures are similar. If they are, write the similarity statement. M P L Q 9 12 R N The triangles are not similar.

7. Example 3: Determine whether the figures are similar
Example 3: Determine whether the figures are similar. If they are, write the similarity statement. WXYZ ~ PQRS

8. HOMEWORK (Day 1)
pg. 476; 8 – 18

9. Scale factor – if two polygons are similar, then the ratio of the lengths of two corresponding sides is called a scale factor.

10. Theorem 8.1
If two polygons are similar, then the ratio of their perimeters is equal to the ratios of their corresponding side lengths.
If KLMN ~ PQRS, then
KL + LM + MN + NK =
PQ + QR + RS + SP KL LM MN NK = = = PQ QR RS SP

11. Example 4: The rectangular patio around a pool is similar to the pool as shown. Calculate the scale factor of the patio to the pool, and find the ratio of their perimeters.
Because the rectangles are similar, the scale factor of the patio to the pool is 48 ft: 32 ft. , which is 3:2 in simplified form.
The perimeter of the patio is 2(24) + 2(48) = 144 feet and the perimeter of the pool is 2(16) + 2(32) = 96 feet
The ratio of the perimeters is
16 ft
24 ft
32 ft
48 ft
144 3
, or 96 2

12. Example 5: Quadrilateral JKLM is similar to PQRS. Find the value of z.

13. Example 6: Parallelogram ABCD is similar to parallelogram GBEF
Example 6: Parallelogram ABCD is similar to parallelogram GBEF. Find the value of y. B E C G A F y 24 D

14. HOMEWORK (Day 2)
pg. 477; 24 – 30, 39 – 42