Chapter 7Similarity

Definition: Ratio

• A quotient of two integers such that b≠0• (must be reduced to lowest terms)

Find the ratio of

1. AB

AD

2. AC

BE

3. CD

ED

24

10

14

8 7

12

A

C D

B E

• The angles of a pentagon are in ratio 4:2:5:5:2, find the measure of each angle

4x+2x+5x+5x+2x = 540 18x = 540 x = 30 120, 60, 150, 150, 60

Definition: Proportion

• Two ratios set equal

• or a:b=c:d

Identify the means and extremes:

•

• Find the third term of a proportion if 4, 9, and 15 are the first, second and fourth term respectively.

Definition: Geometric Mean

• A proportion in which the second and third terms are equal

=

• Find the geometric mean between 5 and 28.

• 18 is the geometric mean between 7 and what number?

Properties of Proportions:

• If , then:a) ad = bc (Means-Extremes Theorem)b) ( Interchanging property)c) (Flipping property)d) (Denominator adding property)

Definition: Similar Polygons

• Two polygons are similar iff,

1) Corresponding angles are congruent2) Corresponding sides are in proportion

If ABCDE ~ NGPHM, then….

Ways to prove triangles similar:

•1) AA~ theorem•2) SSS~ theorem•3) SAS~ theorem

AA~ theorem

• If two angles of one triangle are congruent to corresponding angles of another triangle, then the triangles are similar.

Find BE

How tall is the tree?

• Given: BC // DE• Prove: ∆ABC ~ ∆ADE

Triangle Proportionality Thm

• aka (side splitter thm)

Triangle Angle Bisector Thm