7.1 Ratio and Proportions

Ratio and Proportion _______________________________________ ________________________________________ Word form: Colon form: Fraction form:

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

Find the ratio of AE to BE. 60 A 10 60 E 30 5x B Find the ratio of AE to BE. 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 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 C D 10

The measures of the angles of a triangle are in the ratio of 3:4:5 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

A proportion is a set of two equal ratios: _____________________________________

The Means and Extremes Property: _____________________________________ ______________________________________

Properties of Proportions:

If CE=2, AB=6 and AD=3 then EB=______ 2. If AB=10, DB=8 and CB=7.5 then EB=______

Find BD=______ DA=_____ C E BA=12, BE=10, EC=5 Find BD=______ DA=_____

7.3 Similar Polygons

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

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

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

The ratio of the perimeters of two similar figures is equal to the Scale Factor. 12 z D D` C C` x 2.5 10 5 A` 3 B` A B y a) Scale Factor: a) Find x, y, z:

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

7.4 Proving Triangles are Similar

Postulate 15: ________________________ ___________________________________ A X Y B C

When there are triangles within Trianlges: _______________________________

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

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

A D O B C

7.5 More Similar Triangles

Theorem 7.1: __________________________ ______________________________________ 12 3 5 20

Theorem 7.2: ___________________________ _______________________________________ 12 28 3 7 5 20

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

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

Def of ~ ______________________________ ______________________________________ Means and Extremes Property: __________ _____________________________________

A D B C E

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

7.6 Proportional Lengths

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

Corollary: ____________________________ _____________________________________ a c b d

Triangle Angle Bisector: _______________________________________ c a b d

Examples: 20 5x 10 5

x 10 12 24

x 4 2 x+2