WARM UP

Solve for x

X + 1 = X X 1

You will have to use the Quadratic Formula!

8.2 Similarity

Definition: Similar polygons are polygons in which:

1.The ratios of the measures of corresponding sides are equal.

2.Corresponding angles are congruent.

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.

Proving shapes similar:

1.Similar shapes will have the ratio of all corresponding sides equal.

2.Similar shapes will have all pairs of corresponding angles congruent.

Example:

A

CB

D

E F

648

5 10

12

∆ABC ~ ∆DEF

Therefore: A corresponds to D, B corresponds to E, and C corresponds to F.

1. The ratios of the measures of all pairs of corresponding sides are equal.

AB

DE = 2

1

AC

DF 2

1

BC

EF 2

1= =

Each pair of corresponding angles are congruent.

<B <E <A <D <C <F

∆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

NDM

E

(6,0)(3,0)(0,0)

(0,4)

(0,8)

Given: ABCD ~ EFGH, with measures shown.

1. Find FG, GH, and EH.

AA

B

D

C

G

F

E

H

6

7

4

3

9

2. Find the ratio of the perimeter of ABCD to the perimeter of EFGH.

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.

1

2

First draw and identify corresponding angles.

K

HJ

M

O P

<J comp. <K <K = 50

<K = <M

50 = x + 5

45 = x

<H = <O

90 = y

180 = y

1

2

Given ∆BAT ~ ∆DOT, OT = 15, BT = 12, TD = 9

Find the value of x(AO). A

O

B TD

12

15

9

Hint: set up and use Means-Extremes Product Theorem.

x