Geometry Chapter 7

7.1Ratio and Proportions

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

A6010E60305xBa)Find the ratio of AE to BE.b) Find the ratio of the largest angle ofTriangle A to smallest angle of triangle B.

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

ABCDis a▱AB6D10CAB : BCBC : AD∡A: ∡CAB : Perimeter of ABCD

The measures of the angles of a triangle arein the ratio of 3:4:5. Find the measures ofeach angle.

7.2Properties of Proportions

A proportion is a set of two equal ratios:__________________________________________________________________________

The Means and Extremes Property:•_________________________________________________________________________________________________________________

Properties of Proportions:ab=cd

a 3Using the Proportion = b 5a) 5a=5b) =ba+bc) =b5d)=3

ADIn the figure DB=CEEBDABEC1.If CE=2, AB=6 and AD=3 then EB=______2. If AB=10, DB=8 and CB=7.5 thenEB=______

ADIn the figure DB=CEEBDABEC1.BA=12, BE=10, EC=5Find BD=______ DA=_____

7.3Similar Polygons

______________________________________________________________________________________________________________________________Two polygons are similar if their vertices can bepaired so that:•_________________________________________•_____________________________________________________________________________________________________________________________

BWACVXEDZYGiven: ABCDE∼VWXYZList congruent Angles:List Proportions of sides:

If polygons are similar then the ratio of thelengths of two corresponding sides is calledthe Scale FactorD12CD`yC`xz3022A 30 BA` 50 B`a) Scale Factor: a) Find x, y, z:

The ratio of the perimeters of two similarfigures is equal to the Scale Factor.D12CD`zC`10 5x2.5A y BA` 3 B`a) Scale Factor: a) Find x, y, z:

a) Scale Factor:b) Angle D`=____D560CD`211006C`A4BA`12B`c) Find CB, A`D`, DC:

7.4Proving Triangles areSimilar

Postulate 15: ______________________________________________________________________________________________AXYBC

When there are triangles within Trianlges:•_______________________________•_______________________________

Are the triangles similar?Find the scale factor._______Solve for x=_______3 51 x

Find x=______ and y=______:Scale Factor=____8xy33 4

Given : ACBDADProve : △COA≅△DOBOCB1. 1. Given

7.5More Similar Triangles

Theorem 7.1: ____________________________________________________________________________________________________________________________________________312520

Theorem 7.2: __________________________________________________________________371228520

How do we know what sides of the triangles tocompare?•_______________________________________________________________________________•__________________________________△ABC has sides of 4,5,7 and△XYZhas sides of 16,20,28Are they similar?

What reason are the Triangles ~?6 103 53 56 66 10

Def of ~ __________________________________________________________________________________________________________Means and Extremes Property: ____________________________________________________________________________________

Given : ∡B ≅ ∡DECProve : △ABC∼△DECAD1. 1. GivenBEC

10xy91516Solve for x and y: Scale Factor?____

7.6Proportional Lengths

Divide Proportionally means:________________________________________________________________________________Triangle Proportionality Theorem:____________________________________________________________________________________________________________acbd

Corollary:_________________________________________________________________acbd

Triangle Angle Bisector:____________________________________________________________________________________________________________________________________________________________acbd

Examples:5x20105

1210 x24

x42 x+2