JOURNAL CHAPTER 7&8Amani Mubarak 9-5

Ratio & Proportion Ratio: Is a comparison of two numbers

by division. EXAMPLES

1. The ratios 1 to 2 can be represented as 1:2 and ½2. Ratio of the rectangle may be written as: 3:7:3:7. 7

7

33

3. The ratios 4 to 8 can be represented as 4:8 and 4/8.

Proportion: is an equation representing that two ratios are equal.

How to solve: to solve a proportion you must use the cross product property and solve for the missing letter.

EXAMPLES1. a = c ad=bc

b d

Both ratios and proportions are similar because they use fractions to compare things.

Similar Polygons

Figures that are similar have the same shape but not necessarily the same size.

Two polygons are similar polygons if and only if their corresponding angles are congruent and their corresponding side lenghts are proportional.

Scale factor: describes how much the figure is enlarged or reduced. K: (a,b)→(ka,kb)

EXAMPLES

Similar Triangles Postulate 7-3-1 (AA similarity): If two angles of

one triangle are congruent to two angles of another triangle, then the triangles are similar.

Theorem 7-3-2 (SSS similarity): If the three sides of one triangle are proportional to the three corresponding sides of another triangle, then the triangles are similar.

Theorem 3-3-3 (SAS similarity): If two sides of one triangle are proportional to two sides of another triangle and their included angles are congruent, then the triangles are similar.

How to use similar triangles to perform indirect measurement

To make an indirect measurement by using similar triangles you use the given measurements in order to find the missing side.

EXAMPLES

How to use the scale factor to find the perimeter and area of a new similar figure

To find the scale factor for the perimeter and areas of similar figures you need to see the corresponding sides which are proportional and the corresponding angles are equal. The scale factor describes the difference between the side it also describes how much a figure is enlarged or reduced.

Trigonometric ratios Trigonometric ratio: is a ratio of two sides of a

right triangle. SINE-the sine of an angle is the ratio of the

lenght of the leg opposite the angle to the length of the hypotenuse.

COSINE- the cosine of an angle is the ratio of the length of the leg adjacent to the angle to the length of the hypotenuse.

TANGENT- 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.

EXAMPLES

Angle of Elevation

The angle of elevation is the angle that forms between the horizontal line and the line of sight to a point above the line.

Angle of Depression The angle of depression is the angle

that forms between the horizontal line and the line of sight to a point that is below that line.

_____(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.