Journal 7 & 8By: Maria Jose Diaz-Duran

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

Ratio: compares 2 numbers by division. Proportion: an equation stating that two

ratios are equalThey are related since you use proportion to check the ratio so you kind of use both to find the answer.To solve a proportion you need to cross multiply.To see if its equal you need to rearrange it a later on see if it gives you the same answer.

Examples:

Describe what it means for two polygons to be similar. What is a scale factor? For two polygons to be similar it means

they have the same shape but no necessarily the size

Similar polygons: iff their corresponding angles are congruent and their corresponding sides are proportional.

Scale Factor: the ratio of any two corresponding lengths in two similar geometric figures. Describes how much the figure is enlarged or reduced .

Examples:

http://eigthgrademathmocity2.wikispaces.com/file/view/Dtigers.gif/75151493/Dtigers.gif

Describe how to find the scale factor for the perimeter and areas of similar figures The ratio of the perimeter for similar

figure is equal the ratio of similarity.

The ratio of the area is equal to the (Ratio of similarity 2)

Examples:

Describe how to use similar triangles to make an indirect measurement.

Indirect Measurement: any method to use formulas, similar figures or proportions to measure any object.

Examples:

http://www.encyclo.co.uk/img/math/indirect_m6%5B1%5D.gif

Describe the right triangle altitude proportionality theorem. The altitude to the hypotenuse of a

right triangle forms two triangles that are similar to each other and to the original triangle.

So there will be 3 triangles that are similar

Examples:

Describe the three trigonometric ratios. Explain how they can be used to solve a right triangle. What does it mean to solve a triangle? Trigonometric ratio: a ratio of two sides

of a right triangle.Three Trigonometric Ratios:

The sine if an angle is the ratio of the length of the leg opposite the angle to the length of the hypotenuse

The cosine of an angle is the ratio of the length of the leg adjacent to the angle to the length if the hypotenuse

The tangent of an angle is the ratio of the length of the leg opposite the angle to the length of the leg adjacent to the angle.

To find an angle you can use the inverse of the trigonometric functions.

Examples:

Compare an angle of elevation with an angle of depression. How are each used? Angle of elevation: the angle formed by

a horizontal line and a line of sight to a point above the line.

Angle of depression: the angle formed by a horizontal line and a line of sight to a point below the line.

Examples:

http://rchsbowman.files.wordpress.com/2009/02/021209-0347-geometrynot2.png?w=405&h=184