7 1 Ratio and Proportions Ratio and Proportion

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7. 1 Ratio and Proportions

7. 1 Ratio and Proportions

Ratio and Proportion • ________________________________________ • ____________________ Word form: Colon form: Fraction form: ____________________

Ratio and Proportion • ________________________________________ • ____________________ Word form: Colon form: Fraction form: ____________________

1. A poster is 3 feet long and 20 inches wide. Find the ratio

1. A poster is 3 feet long and 20 inches wide. Find the ratio of length to width. a) Comparing feet: b) Comparing inches:

60 A 60 30 10 E 5 x B a) Find the ratio of

60 A 60 30 10 E 5 x B a) Find the ratio of AE to BE. b) Find the ratio of the largest angle of Triangle A to smallest angle of triangle B.

3. A telephone pole 7 meters tall snaps into two parts. The ratio of

3. A telephone pole 7 meters tall snaps into two parts. The ratio of the two parts is 3: 2. Find the length of each part.

A B 6 D 10 C

A B 6 D 10 C

The measures of the angles of a triangle are in the ratio of 3:

The measures of the angles of a triangle are in the ratio of 3: 4: 5. Find the measures of each angle.

7. 2 Properties of Proportions

7. 2 Properties of Proportions

A proportion is a set of two equal ratios: _____________________________________

A proportion is a set of two equal ratios: _____________________________________

The Means and Extremes Property: • ______________________________________

The Means and Extremes Property: • ______________________________________

Properties of Proportions:

Properties of Proportions:

A D B E C 1. If CE=2, AB=6 and AD=3 then EB=______ 2.

A D B E C 1. If CE=2, AB=6 and AD=3 then EB=______ 2. If AB=10, DB=8 and CB=7. 5 then EB=______

A D B E 1. BA=12, BE=10, EC=5 2. Find BD=______ DA=_____ C

A D B E 1. BA=12, BE=10, EC=5 2. Find BD=______ DA=_____ C

7. 3 Similar Polygons

7. 3 Similar Polygons

__________________________________________ Two polygons are similar if their vertices can be paired so that: •

__________________________________________ Two polygons are similar if their vertices can be paired so that: • __________________________________________

B W A C E D List congruent Angles: List Proportions of sides: V

B W A C E D List congruent Angles: List Proportions of sides: V X Z Y

If polygons are similar then the ratio of the lengths of two corresponding sides

If polygons are similar then the ratio of the lengths of two corresponding sides is called the Scale Factor 12 D C x z A 30 B a) Scale Factor: D` 30 y C` 22 A` 50 B` a) Find x, y, z:

The ratio of the perimeters of two similar figures is equal to the Scale

The ratio of the perimeters of two similar figures is equal to the Scale Factor. 12 D C 10 5 A y B a) Scale Factor: D` z x C` 2. 5 A` 3 B` a) Find x, y, z:

a) Scale Factor: D b) Angle D`=____ C 60 5 A 4 B c)

a) Scale Factor: D b) Angle D`=____ C 60 5 A 4 B c) Find CB, A`D`, DC: D` 21 C` 100 6 A` 12 B`

7. 4 Proving Triangles are Similar

7. 4 Proving Triangles are Similar

When there are triangles within Trianlges: • _______________________________

When there are triangles within Trianlges: • _______________________________

Are the triangles similar? Find the scale factor. _______ Solve for x=_______ 3 1

Are the triangles similar? Find the scale factor. _______ Solve for x=_______ 3 1 5 x

Find x=______ and y=______: Scale Factor=____ x 8 3 y 3 4

Find x=______ and y=______: Scale Factor=____ x 8 3 y 3 4

A D O C B

A D O C B

7. 5 More Similar Triangles

7. 5 More Similar Triangles

How do we know what sides of the triangles to compare? • ________________________________________ •

How do we know what sides of the triangles to compare? • ________________________________________ • _________________

What reason are the Triangles ~? 6 10 3 3 5 5 6 6

What reason are the Triangles ~? 6 10 3 3 5 5 6 6 6 10

A D B E C

A D B E C

10 9 x y 15 16 Solve for x and y: Scale Factor? ____

10 9 x y 15 16 Solve for x and y: Scale Factor? ____

7. 6 Proportional Lengths

7. 6 Proportional Lengths

Divide Proportionally means: ________________________________________ Triangle Proportionality Theorem: ____________________________________ a b c d

Divide Proportionally means: ________________________________________ Triangle Proportionality Theorem: ____________________________________ a b c d

Triangle Angle Bisector: _______________________________________ c a b d

Triangle Angle Bisector: _______________________________________ c a b d

Examples: 20 5 x 10 5

Examples: 20 5 x 10 5

x 10 12 24

x 10 12 24

x 2 4 x+2

x 2 4 x+2