**Ratio**--a
comparison of 2 quantities example: 3:4 or 3/4

**Example:**

* If a class of 20 has
14 boys in it...*

write the ratio of ** boys** to

write the ratio of ** girls** to

write the ratio of ** boys** to

**
Simplifying Ratios: (write both
quantities in the same units before you simplify the fraction)**

**
There are conversions on p730 and p731 into your
textbook and on page r10 in your student planner if you need to look any of
them up.**

** Examples:**

3 pounds : 12 ounces

6 days : 2 weeks

20 feet : 3 years

1 mile : 2640 feet

** Extended
Ratio**--comparison of 3 or more numbers

** example:** 3:4:5

**Example:**

** What is the ratio of the
angles in the triangle below?**

** **

**Example:**

**Three ****
sides of a
triangle are in the extended ratio of 9:8:7 and the triangle has a
perimeter
of 144.**

**Find the ****
length of each side
and list them from shortest to longest.**

**Example:**

**Three ****
angles of a
triangle are in the extended ratio of 5:7:8**

**Find ****
each angle measure and list
them from smallest to largest.**

**Proportion**--an
equality relating two ratios ex 3/4 = 6/8

**Can
be solved by cross multiplication**

**Examples:**

**Means
and Extremes**--Names for the parts of a proportion.

__example__

__3__
= __x
__5 15

* extremes*
of the proportion.

5 and x are called the

Values, variables or expressions in the upper left and lower right positions of the proportion are the extremes.

Values, variables or expressions in the lower left and upper right positions of the proportion are the means.

**The Geometric Mean is
found using this concept.**

Find the Geometric Mean of 4 and 9

__4__
= __x
__x
9

__Some Tricks with
proportions:__

1. The means (or extremes) can be exchanged and the proportion is still true.

2. Reciprocal Rule

3. Add up (or subtract up) Rule

**Examples:**

**A model house is 30 inches long and the
actual house is 48 feet long. Find the scale factor. (this is a ratio)**

**A school has 108 teachers and 1900
students. What is the ratio of students to EACH teacher? ***(how
many students per 1 teacher?)*

**Find the ratio of AE to DI:**

**Find the ratio of IF to CF:**

**Find the ratio of CK to DF:**

__Section
6.2 Similar Polygons__

**
**

Polygons
of the same shape, but different
in size are considered to be ** similar**.
(example: stop signs {octagons} of different sizes.

**Corresponding
angles** must all be **congruent** and **
corresponding
sides** must all be

__Example__

__Example__

__Example__

Are
the two __ rectangles__ similar? If so, what is the scale factor?

__Section
6.3 Similar Triangles__

**Angle
Angle (AA) Similarity**:
If two angles of one triangle are congruent to two angles of another triangle,
then the triangles are similar.

**Side
Side Side (SSS) Similarity**: If the measures of the
corresponding sides of two triangles are **proportional**,
then the triangles are similar.

**Side
Angle Side (SAS) Similarity**: If the measures of two
sides of one triangle are proportional to
two corresponding sides of a second triangle and the included
angles are congruent, then the triangles are similar.

__Example__

A person that is 2 yards tall casts a shadow of 3 yards, while at the same time a tree casts a shadow of 40 yards.

What is the height of the tree?

__Section
6.4 Parallel Lines and Proportional Parts__

**Triangle
Proportionality Theorem**:
If a line is parallel to one side of a triangle and intersects the other two
sides, then it divides these sides into segments of proportional lengths.**
**

**
**

**Triangle
Proportionality Theorem Converse**: If
a line intersects two sides of a triangle and divides these sides into
corresponding segments of proportional lengths, then the line is parallel to the
third side of the triangle.

Is the red segment parallel to the base of the triangle?

**Midsegment**--a
segment whose endpoints are the midpoints of two sides.

**
Triangle
Midsegment Theorem: **A
midsegment of a triangle is parallel to one side of a triangle and is 1/2 the
length of that side.

**Proportional
Parts of Parallel Lines**: The transversals are cut
proportionally by the parallel lines.

__Section
6.5 Parts of Similar Triangles__

** Proportional
Perimeters Theorem**:
If two triangles are similar, then the perimeters are proportional to the
measures of corresponding sides.

**Corresponding
Altitudes**: If two triangles are similar, then the measures of
corresponding altitudes are proportional to the measures of corresponding sides.

**Corresponding
Angle Bisectors**: If two triangles are similar, then the
measures of corresponding angle bisectors are proportional to the measures of
corresponding sides.

**Corresponding
Medians**: If two triangles are similar, then the measures of
corresponding medians are proportional to the measures of corresponding sides.

**Angle
Bisector Theorem**: An angle bisector in a triangle separates the
opposite side into segments that have the same ratio as the other two sides.

** **

**
**

**
**