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**Ratios, Proportions, AND Similar Figures 8.1-8.2**

Today’s Goal(s): To write ratios and solve proportions. To identify and apply similar polygons.

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**Ratios A ratio is a comparison of two quantities.**

The ratio of a to b can be written 3 ways: when b 0

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Proportions A proportion is an equation stating two ratios are equivalent. a : b = c : d Read: “a is to b as c is to d”

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**Do you remember… Means and Extremes**

Cross-Product Property The cross products of a proportion are EQUAL. ad = bc

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**Solve each proportion using the cross-product property.**

a.) b.) c.)

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**Similar Figures have the same shape, but not necessarily the same size.**

New symbol: ~ means “is similar to” corresponding angles are congruent ( ) corresponding sides are proportional.

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**Similarity Ratio The ratio of the lengths of corresponding sides.**

Determine whether the triangles are similar. If they are, write a similarity statement and give the similarity ratio.

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**LMNO ~ QRST Find x & write the similarity ratio.**

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8.2 Extra Examples

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** You try this one on your own!**

8.2 Extra Examples You try this one on your own!

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Scale Drawings You use proportions all the time in scale drawings. In scale drawings, the scale compares each length in the drawing to the actual length. Example: Suppose you want to make a scale drawing with a scale of 1 in. = 4 ft. What are the dimensions of a 14 ft. by 10 ft. room?

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Ex.2 cont…

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Benchmark Review Write each in simplest radical form: a.) b.) c.) d.)

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**Similarity in Right Triangles Toolkit #8.4**

Today’s Goal(s): To find and use relationships in similar right triangles.

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**Page 438 49. <E 55. W(-b,c) Z(-b,-c) 50. <P 56. W(-b,c) Z(-a,0)**

51. <Y <x<24 52. ZY 53. EZ 54. YZ

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Geometric Mean The geometric mean of two positive numbers a and b is the positive number x such that therefore

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**Find the geometric mean of 4 and 18.**

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Fill in the angles 50

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Now use letters y x

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**Stop and Think!! How many similar right triangles are formed when you drop a “height” (altitude)?**

x z y

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**Take Two Triangles and write the proportion**

c a b d e c a a b d d+e

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**Take the “big” with the right.**

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Big with the left

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**Take the Left with the Right**

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**Right Triangle “Car” Problem (Understanding the set-up) **

HOME RHS

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**Right Triangle “Car” Problem Time to drive…**

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Examples: #1

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Examples: #2

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Examples: #3

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Examples: #4

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**Let’s practice finding the geometric mean of a pair of numbers! **

Your answer MUST be in SIMPLEST RADICAL FORM! 4 and 9 4 and 10 5 and 125 7 and 9 x = 6 x = 210 x = 25 x = 37

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You Try #1 Solve for x. x = 9

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You Try #2 Solve for x. x = 63

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You Try #3 Solve for x. x = 12

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You Try #4 Solve for x. x = 10

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You Try #5 Solve for x. x = 60

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You Try #6 Solve for x. x = 20

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**Cool Down Find the average of 80 and 90.**

Find the arithmetic mean of 80, 90, 100. Find the geometric mean of 12 and 3. Draw, label and write the geometric mean proportion for x, y, and z.

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EXAMPLE 2 Find the scale factor Determine whether the polygons are similar. If they are, write a similarity statement and find the scale factor of ZYXW.

EXAMPLE 2 Find the scale factor Determine whether the polygons are similar. If they are, write a similarity statement and find the scale factor of ZYXW.

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