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Daniela Morales Leonhardt 9-5. _____(0-10 pts) Describe a ratio. Describe a proportion. How are they related? Describe how to solve a proportion. Describe.

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Presentation on theme: "Daniela Morales Leonhardt 9-5. _____(0-10 pts) Describe a ratio. Describe a proportion. How are they related? Describe how to solve a proportion. Describe."— Presentation transcript:

1 Daniela Morales Leonhardt 9-5

2 _____(0-10 pts) Describe a ratio. Describe a proportion. How are they related? Describe how to solve a proportion. Describe how to check if a proportion is equal. Give 3 examples of each.

3  A ratio is a comparison between two numbers or quantities.  They can be expressed as A to B, A:B, A is to B, or A/B.  There can be more than 2 numbers being compared.

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8  A proportion is an equation stating that two ratios are equal.  Parts of a proportion:

9 To solve a proportion with one variable, you cross multiply both ratios. Then you isolate the variable in the given equation, and solve to find it. If there are two variables in the proportion, solve with square roots. 4 x 6 = 3n 24= 3n 24/3 8=n

10  To check If a proportion is equal, multiply both extremes together and both means together. If both products are equal, then the proportion is equal. If not, re-do the problem or it’s not even a proportion. 4 x 6 = 24 3 x 8 = 24 Equal.

11  4/8 = 6/y  4y= 8 x 6  4y = 48  48/4  y= 12  4/8=6/12  4 x 12 = 48  8 x 6 = 48  Equal.

12  7/20 = 2/r  7r= 40  40/7  r = 5.7  7 x 5.7 = 40 (rounded 39.9)  20 x 2 = 40

13  Polygons are similar if and only if their corresponding angles are congruent and their corresponding sides are proportional.

14 12 18 2 2 x Example 1. The each side of the larger rectangle is 6 times as larger as each of the corresponding sides of its similar rectangle. If 6 x 2 is 18, and 18 divided by 6 is 3 then x = 3.

15 A scale factor is one that counts how much a shape has been enlarged or reduced. Dilation refers to enlarging or shrinking without changing shape. A dilation larger than one refers to increasing size, a negative one refers to shrinking.

16 What’s the proportion of AB to DF? 5/10, which can be reduced to ½.

17  What’s indirect measurement?  Indirect measurement’s when you use similar polygons, formulas, or proportions to find out the measurement of something else.  You wouldn’t want to use a tape measure to measure a tall tree, so you can use shadows.  You do this by placing a reflective object (such as a mirror) on the ground and back up to see when you can see the object’s peak’s reflection. You then measure yourself, the distance between you and the mirror and then the object ant the mirror then your height and solve the proportions.

18 6/8 = a/12 6 x 12 = 8a 72 = 8a 72/8 A= 9 3 x 9 = 27 The statue is 27 feet tall

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20 _____(0-10 pts) Describe a ratio. Describe a proportion. How are they related? Describe how to solve a proportion. Describe how to check if a proportion is equal. Give 3 examples of each. _____(0-10 pts) Describe what it means for two polygons to be similar. What is a scale factor? Give at least 3 examples of each. _____(0-10 pts) Describe how to use similar triangles to perform an indirect measurement. Why is this an important skill? Give at least 3 examples. _____(0-10 pts) Describe how to use the scale factor to find the perimeter and area of a new similar figure. Give 3 examples of each, 3 for perimeter, 3 for area. _____(0-10 pts.) Describe the three trigonometric ratios. Explain how they can be used to solve a right triangle. What does it mean to solve a triangle? Give at least 3 examples of each. _____(0-10 pts.) Compare an angle of elevation with an angle of depression. How are each used? Give at least 3 examples of each.


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