1. WARM UP
Solve for x
X + 1 = X X
You will have to use the Quadratic Formula!

2. 8.2 Similarity 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 6 4 C E F B 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.
(0,8) C E
(0,4) N M D
(0,0)
(3,0)
(6,0)

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

10. T61: The ratio of the perimeters of two similar polygons equals the ratio of any pair of corresponding sides.
Given that ∆JHK ~ ∆POM, <H = 90, <J = 40, m<M = x+5, and m<O = y, find the values of x and y.
First draw and identify corresponding angles.

11. <J comp. <K  <K = 50 <K = <M 50 = x + 5 45 = xH O
<J comp. <K  <K = 50
<K = <M
50 = x + 5
45 = x

12. <H = <O
90 = y
180 = y

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