1 / 20

Daniela Morales Leonhardt 9-5

JOURNAL CHAPTERS 7&8. Daniela Morales Leonhardt 9-5. TOPIC 1:. _____(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. What’s A Ratio?.

wilkinson-junior
Download Presentation

Daniela Morales Leonhardt 9-5

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. JOURNAL CHAPTERS 7&8. Daniela Morales Leonhardt 9-5

  2. TOPIC 1: _____(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. What’s A Ratio? • 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.

  4. Examples Fact: Older TV sets had a standard measurement Of , meaning the width of the TV Is ¾ times the height of it. 3:4 If there are 26 cardboard boxes And 15 metal boxes, the ratio of card- Board boxes to metal boxes would be 26:15

  5. Examples– What’s the ratio of This shape? 13 10:13:7:4 10 7 4

  6. Examples– What’s the ratio of This shape? 1 14 17 2 2 17:1:14:2:2:10 10

  7. Examples– What’s the ratio of This shape? This shape is a square. Ratio: 11:11:11:11 11

  8. What’s a proportion? • A proportion is an equation stating that two ratios are equal. • Parts of a proportion: Meansl Extremes d & y x & f x/y=d/f

  9. How do you solve a proportion? 4 n 3 6 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. How to check if a proportion is equal • 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. Example: (from past slide) 4 x 6 = 24 3 x 8 = 24 Equal.

  11. Examples • 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. How to check if a proportion is equal • 7/20 = 2/r • 7r= 40 • 40/7 • r = 5.7 • 7 x 5.7 = 40 (rounded 39.9) • 20 x 2 = 40

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

  14. 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. 18 12 12 18 2 2 x

  15. Scale Factor 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. 9 D B 5 10 A F 9 What’s the proportion of AB to DF? 5/10, which can be reduced to ½.

  17. Simple Triangles for Indirect Measurement • 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. How tall is HE? 6/8 = a/12 6 x 12 = 8a 72 = 8a 72/8 A= 9 3 x 9 = 27 The statue is 27 feet tall 3x 12 ft. 8 ft. 6 ft

  19. _____(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.

More Related