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Journal 7 – 8

Journal 7 – 8 . Ratio: is the comparison of two numbers by division Ratio of two numbers can be shown like this; a to b, a:b, or a/b Proportion: equation that says two ratios are equal To solve a proportion, you have to cross multiply . Describe a ratio/ describe a proportion.

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Journal 7 – 8

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  1. Journal 7 – 8

  2. Ratio: is the comparison of two numbers by division Ratio of two numbers can be shown like this; a to b, a:b, or a/b Proportion: equation that says two ratios are equal To solve a proportion, you have to cross multiply Describe a ratio/ describe a proportion

  3. Ratio/proportion examples

  4. If to polygons are similar it means that their corresponding angles are congruent and their corresponding side lengths are proportional, Same shape, different size Scale factor: is the ratio of two corresponding lengths in two similar figures, it shows how much a figure has been enlarged or reduced What it means for two polygons to be similar?, what is scale factor?

  5. Similar polygons, Scale factor – examples

  6. How to find the scale factor for perimeter and area of similar figures

  7. Indirect measure: method that uses formulas, similar figures and/or proportions to measure any object How to use similar triangles to make an indirect measurement

  8. Indirect proof – examples

  9. Right triangle altitude proportionally theorem: the altitude to the hypotenuse of a right triangle, creates two triangles that are similar to the original triangle and to each other Proportions can be used in real life when you have 20ft of rope to cross a river, and you need to know how wide the river is, you can use proportions to find out if you have enough rope Describe the right triangle altitude proportionally theorem

  10. Right triangle proportionally theorem – examples

  11. A trigonometric ratios is a ratio of two sides of a right triangle SOH CAH TOA Sin= opposite/hypotenuse Cos= adjacent/hypotenuse Tan= opposite/adjacent To solve a triangle is to find out all the lengths of the sides and the measures of the angles Three trigonometric ratios

  12. The trigonometric ratios are used to find lengths but you can use the inverse to find the measure of angles Cos-1(adjacent/hypotenuse)=angle Tan-1(opposite/adjacent)=angle Sin-1(opposite/hypotenuse)=angle Trigonometric ratios

  13. Trigonometric ratios – examples

  14. Angle of elevation: the angle made with the horizontal looking up Angle of depression: the angle from the horizontal down to an object below Compare, angle of elevation and angle of depression

  15. Elevation and depression angles – examples

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