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JOURNAL 7 – 8
DESCRIBE A RATIO/ DESCRIBE A PROPORTION
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
RATIO/PROPORTION EXAMPLES
WHAT IT MEANS FOR TWO POLYGONS TO BE SIMILAR?, WHAT IS SCALE FACTOR?
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
SIMILAR POLYGONS, SCALE FACTOR – EXAMPLES
HOW TO FIND THE SCALE FACTOR FOR PERIMETER AND AREA OF SIMILAR FIGURES
HOW TO USE SIMILAR TRIANGLES TO MAKE AN INDIRECT MEASUREMENT
Indirect measure: method that uses formulas, similar figures and/or proportions to measure any object
INDIRECT PROOF – EXAMPLES
DESCRIBE THE RIGHT TRIANGLE ALTITUDE PROPORTIONALLY THEOREM
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
RIGHT TRIANGLE PROPORTIONALLY THEOREM – EXAMPLES
THREE TRIGONOMETRIC RATIOS
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
TRIGONOMETRIC RATIOS
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 – EXAMPLES
COMPARE, ANGLE OF ELEVATION AND ANGLE OF DEPRESSION
Angle of elevation: the angle made with the horizontal looking up
Angle of depression: the angle from the horizontal down to an object below
ELEVATION AND DEPRESSION ANGLES – EXAMPLES