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