1. 7.1 Ratio and Proportion
Geometry
Ms. Kelly
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2. Objectives 7.1 Ratio and Proportion 7.2 Properties of Proportions
Express a _____ in simplest form.
Solve for an unknown term in a given proportion.
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3. Real Life Applications
Let’s list on the board where you find ratios and proportions in real life. (1st block)
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4. Real Life Applications
Let’s list on the board where you find ratios and proportions in real life. (3rd block)
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5. Definitions Ratio What is looks like…..
The ratio of one number to another is the _______ when the first number is ______ by the second.
Its usually expressed in simplest form.
The ratio of 8 to 12 is ______, or ______.
If y ≠ 0, then the ration of x to y is _______.
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6. Ex. 1: Simplifying Ratios
Simplify the ratios:
12 cm b. 6n2 c. 9p
4 cm n p
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7. 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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8. 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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9. 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°.
2x°
3x° x°
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10. 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°.
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11. More examples of a:b Find the ratio and express in simplest form.
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12. Proportion What it is… What is looks like….
A proportion is an equation stating that ____ ratios are equal.
When three of more ratios are equal, you can write an extended proportion.
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13. Closure to 7.1 Ticket to stay in class Answers
Three numbers aren’t known but the ratio of the numbers is 1:2:5. Is it possible that the numbers are:
10, 20 and 50?
3, 6, and 20?
x, 2x, 5x
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14. Classwork Page 243 1-4, 8-11 on mini-white boards or whiteboards
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15. Properties of Proportions
7.2
Properties of Proportions
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16. 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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17. Properties of proportions
CROSS PRODUCT PROPERTY. The product of the extremes equals the product of the means. If
 = , then ad = bc
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18. Properties of proportions
RECIPROCAL PROPERTY. If two ratios are equal, then their reciprocals are also equal.
If  = , then =  b a
To solve the proportion, you find the value of the variable.
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19. Ex. 4: Solving Proportions5
Write the original proportion.
Reciprocal prop.
Multiply each side by 4
Simplify. = x 7 4 x 7 4 = 4 5 28 x = 5
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20. Ex. 5: Solving Proportions3 2
Write the original proportion.
Cross Product prop.
Distributive Property
Subtract 2y from each side. =
y + 2 y
3y = 2(y+2)
3y = 2y+4 y 4 =
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21. Example 6 - Factoring
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22. Example 7 In the figure, If CE = 2, EB = 6 and AD = 3, then DB = ___
If AB = 10, DB = 8, and CB = 7.5, then EB =___
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23. Homework Page 243-244 1-14, 21-30 Page 247 – 248 9-29 odds, 33-38
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