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7.1 Ratio and ProportionGeometry

Ms. Kelly

Objectives

7.1 Ratio and Proportion Express a _____ in

simplest form.

7.2 Properties of Proportions Solve for an unknown term

in a given proportion.

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Real Life Applications Let’s list on the board where you find ratios

and proportions in real life. (1st block)

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Real Life Applications Let’s list on the board where you find ratios

and proportions in real life. (3rd block)

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Definitions

Ratio The ratio of one number to

another is the _______ when the first number is ______ by the second.

Its usually expressed in simplest form.

What is looks like….. The ratio of 8 to 12 is

______, or ______. If y ≠ 0, then the ration of

x to y is _______.

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Ex. 1: Simplifying Ratios Simplify the ratios:

a. 12 cm b. 6n2 c. 9p

4 cm 18n 18p

Example 2

Find the ratio of OI to ZD Using the same trapezoid…

Find the ratio of the measure of the smallest angle of the trapezoid to that of the largest angle.

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Ratios in Form a:b Sometimes the ratio of a to b is written in the form a:b. This

form can also be used to compare three of more numbers, like a:b:c.

Example: The measures of the three angles of a triangle are in the ratio 2:2:5. Find the measure of each angle.

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Ex. 3: Using Extended Ratios The measures of the angles

in ∆JKL are in the extended ratio 1:2:3. Find the measures of the angles.

Begin by sketching a triangle. Then use the extended ratio of 1:2:3 to label the measures of the angles as x°, 2x°, and 3x°.

J

K

L

x°

2x°

3x°

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Solution:Statement

x°+ 2x°+ 3x° = 180°

6x = 180

x = 30

Reason

Triangle Sum Theorem

Combine like terms

Divide each side by 6

So, the angle measures are 30°, 2(30°) = 60°, and 3(30°) = 90°.

More examples of a:b Find the ratio and express in simplest form.

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Proportion

What it is… A proportion is an equation

stating that ____ ratios are equal.

When three of more ratios are equal, you can write an extended proportion.

What is looks like….

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Closure to 7.1

Ticket to stay in class

Three numbers aren’t known but the ratio of the numbers is 1:2:5. Is it possible that the numbers are:

1. 10, 20 and 50?

2. 3, 6, and 20?

3. x, 2x, 5x

Answers

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Classwork Page 243 1-4, 8-11 on mini-white boards or

whiteboards

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7.2 Properties of Proportions

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Using Proportions An equation that

equates two ratios is called a proportion. For instance, if the ratio of a/b is equal to the ratio c/d; then the following proportion can be written:

= Means Extremes

The numbers a and d are the extremes of the proportions. The numbers b and c are the means of the proportion.

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Properties of proportions1. CROSS PRODUCT PROPERTY. The

product of the extremes equals the product of the means.

If

= , then ad = bc

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Properties of proportions2. RECIPROCAL PROPERTY. If two ratios

are equal, then their reciprocals are also equal.

If = , then = ba

To solve the proportion, you find the value of the variable.

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Ex. 4: Solving Proportions

4x

57=

Write the original proportion.

Reciprocal prop.

Multiply each side by 4

Simplify.

x4

75=

4 4

x = 285

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Ex. 5: Solving Proportions

3y + 2

2y=

Write the original proportion.

Cross Product prop.

Distributive Property

Subtract 2y from each side.

3y = 2(y+2)

y = 4

3y = 2y+4

Example 6 - Factoring

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Example 7 In the figure,

a. If CE = 2, EB = 6 and AD = 3, then DB = ___

b. If AB = 10, DB = 8, and CB = 7.5, then EB =___Slide #22

Homework Page 243-244 1-14, 21-30 Page 247 – 248 9-29 odds, 33-38

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