1. NOTES 8.2
Similarity

2. Definition: Similar polygons are polygons in which:
The ratios of the measures of corresponding sides are equal.
Corresponding angles are congruent.

3. Similar figures: figures that have the same shape but not necessarily the same size.
Dilation: when a figure is enlarged to be similar to another figure.
Reduction: when a figure is made smaller it also produces similar figures.

4. Proving shapes similar:
Similar shapes will have the ratio of all corresponding sides equal.
Similar shapes will have all pairs of corresponding angles congruent.

5. Example: ∆ABC ~ ∆DEF = = =8 12 4 6 B C E F 5 10
Therefore: A corresponds to D, B corresponds to E, and C corresponds to F.
The ratios of the measures of all pairs of corresponding sides are equal. = = =

6. Each pair of corresponding angles are congruent.
<B <E <A <D <C <F

7. ∆MCN is a dilation of ∆MED, with an enlargement ratio of 2:1 for each pair of corresponding sides. Find the lengths of the sides of ∆MCN. C
(0,8) 8
MC =
MN =
CN = E
(0,4) 6 10 D N M
(0,0)
(3,0)
(6,0)

8. Given: ABCD ~ EFGH, with measures shown.
1. Find FG, GH, and EH.
FG =
GH =
EH = 6 B 6 F 9 4 A
4.5 A E C 7 3 D G
10.5 H
PABCD = 20 PEFGH = 30
= 2 3
2. Find the ratio of the perimeter of ABCD to the perimeter of EFGH.

9. Theorem 61: The ratio of the perimeters of two similar polygons equals the ratio of any pair of corresponding sides.

10. Given ∆BAT ~ ∆DOT OT = 15, BT = 12, TD = 9 Find the value of x(AO).
AT = BT OT TD O 15
x = D
x = 5 B 12 9 T
Hint: set up and use Means-Extremes Product Theorem.