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ratio

proportion

similar

scale factor

The ____ of one number to another is the quotient when the fi…

A _____ is an equation stating that two ratios are equal. (ex…

Two polygons are ____ if their vertices can be paired so that…

If two polygons are similar, then the ratio of the lengths of…

ratio

The ____ of one number to another is the quotient when the fi…

proportion

A _____ is an equation stating that two ratios are equal. (ex…

Ratio

Proportions

Means extreme property

Similar polygons

One number to another is the quotient where the first number…

Is an equation stating that two ratios are equal.

The product of the means is equal to the product of extremes.

Two polygons are similar if their vertices can be paired such…

Ratio

One number to another is the quotient where the first number…

Proportions

Is an equation stating that two ratios are equal.

King Henry Died Unexpectedly Drinking…

Extremes

Mean

Means-Extremes Property

Kilo Hecto Deca Unit Deci Centi Milli

First and last terms of proportion

Middle terms of proportion

Cross-Multiplying

King Henry Died Unexpectedly Drinking…

Kilo Hecto Deca Unit Deci Centi Milli

Extremes

First and last terms of proportion

MEPP - Means-Extremes Property of Prop…

Property of Proportions A

Property of Proportions B

Property of Proportions C

the product of the extremes equals the product of the means

a/b=c/d = ad=bc

a/b=c/d = a/c=b/d

a/b=c/d = b/a=d/c

MEPP - Means-Extremes Property of Prop…

the product of the extremes equals the product of the means

Property of Proportions A

a/b=c/d = ad=bc

Proportion

Similar polygons

Conditions that make polygons similar

Proportional

an equation stating that two ratios are equal

figures that have the same shape but different size

1.) Corresponding angles are congruent... 2.) Corresponding side…

in the same ratio

Proportion

an equation stating that two ratios are equal

Similar polygons

figures that have the same shape but different size

ratio

proportion

extremes

means

first number divided by second number in simplest form... used t…

eq stating that two ratios are =

if a/b = c/d, a and d are the extremes

if a/b = c/d, b and c are the means

ratio

first number divided by second number in simplest form... used t…

proportion

eq stating that two ratios are =

acute

angle

bisector

collinear

Angle measuring less than 90°.

A figure formed by 2 rays with a common endpoint.

A line or part of a line that divides a segment or angle into…

Means together on the same line

acute

Angle measuring less than 90°.

angle

A figure formed by 2 rays with a common endpoint.

Ratio

Unit ratio

Proportion

Means and extremes

comparison of two numbers... usually written as a fraction... usual…

ration where second number is 1... ex. 3:1, 3/1

a/b=c/d... 2 equal ratios

a is to b as c is to d... a:b = c:d... b,c = means... a,d = extremes

Ratio

comparison of two numbers... usually written as a fraction... usual…

Unit ratio

ration where second number is 1... ex. 3:1, 3/1

Extremes

Mean

AA Similarity Postulate

SAS Similarity Theorem

the first and last of a proportion

the second and third parts of a proportion

If two angles of one triangle are congruent to two angles of…

If an angle of one triangle is congruent to an angle of anoth…

Extremes

the first and last of a proportion

Mean

the second and third parts of a proportion

SAS Similarity Theorem

SSS Similarity Theorem

Triangle Proportionality Theorem

Triangle Angle-Bisector Theorem

If an angle of one triangle is congruent to an angle of anoth…

If the sides of two triangles are in proportion, then the tri…

If a line parallel to one side of a triangle intersects the o…

If a ray bisects an angle of a triangle, then it divides the…

SAS Similarity Theorem

If an angle of one triangle is congruent to an angle of anoth…

SSS Similarity Theorem

If the sides of two triangles are in proportion, then the tri…

similar figures

scale factor

AA similarity

SAS similarity

two figures that have the same shape by (1) Corresponding ang…

the ratio of the lengths of two corresponding sides

If two angles of one triangle are congruent to two angles of…

If an angle of one triangle is congruent to an angle of anoth…

similar figures

two figures that have the same shape by (1) Corresponding ang…

scale factor

the ratio of the lengths of two corresponding sides

Ratio

Extended Ratio

Proportion

Similar Polygons

A comparison between two objects.

A comparison between three or more objects.

A comparison between two ratios.

Two polygons with congruent angles and proportional side leng…

Ratio

A comparison between two objects.

Extended Ratio

A comparison between three or more objects.

Means-extremes Property

A Property of Proportions

AA Similarity Postulate

SAS Similarity Theorem

A reason, use when doing cross multiplication in the statemen…

A reason, use when proving 2 proportions equal to one scale f…

If two angles of one triangle are congruent to two angles of…

If an angle of one triangle is congruent to an angle of anoth…

Means-extremes Property

A reason, use when doing cross multiplication in the statemen…

A Property of Proportions

A reason, use when proving 2 proportions equal to one scale f…

ratio

proportion

similar

scale factor

The ____ of one number to another is the quotient when the fi…

A _____ is an equation stating that two ratios are equal. (ex…

Two polygons are ____ if their vertices can be paired so that…

If two polygons are similar, then the ratio of the lengths of…

ratio

The ____ of one number to another is the quotient when the fi…

proportion

A _____ is an equation stating that two ratios are equal. (ex…

ratio

proportion

similar

scale factor

The ____ of one number to another is the quotient when the fi…

A _____ is an equation stating that two ratios are equal. (ex…

Two polygons are ____ if their vertices can be paired so that…

If two polygons are similar, then the ratio of the lengths of…

ratio

The ____ of one number to another is the quotient when the fi…

proportion

A _____ is an equation stating that two ratios are equal. (ex…

When are two polygons similar?

Find the scale factor of the ratio of…

what is the similarity of two polygons…

is the scale factor of these polygons…

when their corresponding angles are congruent and side length…

triangle ABC~ triangle DEF ... 14/6 = 7/3 ... 7/3 = 20/x ... 7(x)=7x... 3…

rectangle 1: ... p=18... rectangle 2: ... p=36... 5/10=1/2... 4/8= 1/2 ... 18/3…

yes ... 0.4

When are two polygons similar?

when their corresponding angles are congruent and side length…

Find the scale factor of the ratio of…

triangle ABC~ triangle DEF ... 14/6 = 7/3 ... 7/3 = 20/x ... 7(x)=7x... 3…

Ratio

What are ratios expressed in?

Proportion

Terms of proportions

The quotient when one number is divided by another number

Simplest form

An equation stating that two ratios are equal

Each number in a proportion

Ratio

The quotient when one number is divided by another number

What are ratios expressed in?

Simplest form

ratio

proportion

means of a proportion

extremes of a proportion

is a comparison of two numbers and can be written in three di…

An equation stating that two ratios are equal

In the proportion a/b = c/d, b and c are the means

In the proportion a/b = c/d, a and d are the extremes

ratio

is a comparison of two numbers and can be written in three di…

proportion

An equation stating that two ratios are equal

ratio

proportion

means of a proportion

extremes of a proportion

is a comparison of two numbers and can be written in three di…

An equation stating that two ratios are equal

In the proportion a/b = c/d, b and c are the means

In the proportion a/b = c/d, a and d are the extremes

ratio

is a comparison of two numbers and can be written in three di…

proportion

An equation stating that two ratios are equal

Ratio

Proportion

Extremes (of a proportion)

Means (of a proportion)

A comparison of two quantities, a and b, which is written as…

an equation showing that two ratios are equal.

the FIRST and LAST terms in a proportion.

the middle terms in a proportion. (BLUE)

Ratio

A comparison of two quantities, a and b, which is written as…

Proportion

an equation showing that two ratios are equal.

Ratio

Proportion

Extremes

Means

The comparison of two quantities by division. (7-1)

An equation that equates two ratios. (7-1)

The first and last term of a proportion. (7-1)

The inner terms of a proportion. (7-1)

Ratio

The comparison of two quantities by division. (7-1)

Proportion

An equation that equates two ratios. (7-1)

ratio

similar figures

symbol for similarity

similar polygons

a comparison of 2 quantities by division

they have the same shape but not the same size

~

2 polygons are similar polygons if corresponding angles are c…

ratio

a comparison of 2 quantities by division

similar figures

they have the same shape but not the same size

ratio

extended ratio

proportion

extremes

a comparison of two quantities by division

compares three or more numbers

an equation that states two ratios are equal

the first and last numbers in a proportion

ratio

a comparison of two quantities by division

extended ratio

compares three or more numbers

Similar

Similar polygons

Similarity ratio

Similarity transformation

Two figures are similar if they have the same shape but not n…

ow polygons whose corresponding angles are congruent ad whose…

the ratio of two corresponding linear measurements in a pair…

A transformation that produces similar figures.

Similar

Two figures are similar if they have the same shape but not n…

Similar polygons

ow polygons whose corresponding angles are congruent ad whose…

Postulate AAA

Theorem 59 (Page 327)

Theorem 60 (Page 327)

Theorem 61 (Page 334)

If there exists a correspondence between the vertices of two…

In a proportion, the product of the means is equal to the pro…

If the product of a pair of nonzero numbers is equal to the p…

The ratio of the perimeters of two similar polygons equals th…

Postulate AAA

If there exists a correspondence between the vertices of two…

Theorem 59 (Page 327)

In a proportion, the product of the means is equal to the pro…

dilation

similar

similarity ratio

indirect measurement

A transformation that changes the size of a figure but not it…

Same shape, corresponding angles are equal, corresponding sid…

The ratio of the lengths of corresponding sides is the simila…

A method of measuring an object by using formulas, similar fi…

dilation

A transformation that changes the size of a figure but not it…

similar

Same shape, corresponding angles are equal, corresponding sid…

ratio

extended ratio

proportion

extremes

comparison of two quantities by division

compares three or more numbers

an equation that states that two ratios are equal

first and last numbers in a proportion; top left and bottom r…

ratio

comparison of two quantities by division

extended ratio

compares three or more numbers

Diagonal

Theorem 7.1: Polygon Interior Angles T…

Corollary 7.1: Corollary to the Polygo…

Equilateral Polygon

A segment that joins two nonconsecutive vertices of a polygon.

The sum of the measures of the interior angles of a convex n-…

The sum of the measures of the interior angles of a quadrilat…

A polygon in which all sides are congruent.

Diagonal

A segment that joins two nonconsecutive vertices of a polygon.

Theorem 7.1: Polygon Interior Angles T…

The sum of the measures of the interior angles of a convex n-…

Postulate AAA

Theorem 59 (Page 327)

Theorem 60 (Page 327)

Theorem 61 (Page 334)

If there exists a correspondence between the vertices of two…

In a proportion, the product of the means is equal to the pro…

If the product of a pair of nonzero numbers is equal to the p…

The ratio of the perimeters of two similar polygons equals th…

Postulate AAA

If there exists a correspondence between the vertices of two…

Theorem 59 (Page 327)

In a proportion, the product of the means is equal to the pro…

Similar

similar polygons

similarity ratio

angle angle similarity theorem

Two figures that have the same shape, but not necessarily the…

Two polygons whose corresponding angles are congruent and who…

The ratio of two corresponding linear measurements in a pair…

If two angles of one triangle are congruent to two angles of…

Similar

Two figures that have the same shape, but not necessarily the…

similar polygons

Two polygons whose corresponding angles are congruent and who…

7.1 similar (∼)

7.1 similar polygons

7.1 similarity ratio

7.2 similarity transformation

figures that have the same shape but not necessarily the same…

two polygons with corresponding angles that are congruent and…

the ratio of the lengths of the corresponding sides of two si…

a dilation or a composite of one or more dilations and one or…

7.1 similar (∼)

figures that have the same shape but not necessarily the same…

7.1 similar polygons

two polygons with corresponding angles that are congruent and…

Cross-Product Property

Ratio

Proportion

scale-drawing

The product of the extremes is equal to the product of the me…

is a comparison of two quantities

is a statement that two ratios are equal

the SCALE compares each length in the drawing to the actual l…

Cross-Product Property

The product of the extremes is equal to the product of the me…

Ratio

is a comparison of two quantities

Similar

Similar Polygons

Similarity Ratio

Similarity Transformation

have the same shape but not necessarily the same size

Polygons that have the same shape, but not necessarily the sa…

the ratio of the lengths of corresponding sides

dilation or a composite of one or more dilations and one or m…

Similar

have the same shape but not necessarily the same size

Similar Polygons

Polygons that have the same shape, but not necessarily the sa…

In a proportion, the product of the me…

In a proportion, the means may be

In a proportion, the extremes may be

AA Postulate states that

the product of the extremes

interchanged

interchanged

when 2 angles of one triangle are congruent to 2 correspondin…

In a proportion, the product of the me…

the product of the extremes

In a proportion, the means may be

interchanged

ratio

extended ratio

proportion

extremes

comparison of two quantities by division

compares three or more numbers

an equation that states that two ratios are equal

the first and last numbers in a proportion

ratio

comparison of two quantities by division

extended ratio

compares three or more numbers

Corresponding Parts of Similar ∼Polygons

Corresponding Lengths in Similar ∼Poly…

Theorem 8.1: Perimeters of Similar ∼Po…

Theorem 8.2: Areas of Similar ∼Polygons

Corresponding angles of similar polygons are congruent and co…

If two polygons are similar, then the ratio of any two corres…

If two polygons are similar, then the ratio of their perimete…

If two polygons are similar, then the ratio of their areas is…

Corresponding Parts of Similar ∼Polygons

Corresponding angles of similar polygons are congruent and co…

Corresponding Lengths in Similar ∼Poly…

If two polygons are similar, then the ratio of any two corres…

Theorem 50

Theorem 51

Theorem 52

Theorem 53

The sum of measures of the three angles of a triangle is 180.

The measure of an exterior angle of a triangle is equal to th…

A segment joining the midpoints of two sides of a triangle is…

If two angles of one triangle are congruent to two angles of…

Theorem 50

The sum of measures of the three angles of a triangle is 180.

Theorem 51

The measure of an exterior angle of a triangle is equal to th…

Properties of proportions

Similar figures

Similar polygons

Extended proportion

(1) a/b=c/d is = to b/a=d/c... (2) a/b=c/d is = to a/c=b/d... (3) a…

Have the same shape but not necessarily the same sides

If corresponding angles are congruent and if the length of co…

When 3 or more raitos set equal to eachother

Properties of proportions

(1) a/b=c/d is = to b/a=d/c... (2) a/b=c/d is = to a/c=b/d... (3) a…

Similar figures

Have the same shape but not necessarily the same sides

Theorem 5.1 Means-Extremes Property

Theorem 5.2 Reciprocal Property of Pro…

Theorem 5.3 Means Property of Proporti…

Theorem 5.4 Extremes Property of Propo…

If any proportion, the product of the means is equal to the p…

The reciprocals of both sides of a proportion are also propor…

If the means are interchanged in a proportion, a new proporti…

If the extremes are interchanged in a proportion, a new propo…

Theorem 5.1 Means-Extremes Property

If any proportion, the product of the means is equal to the p…

Theorem 5.2 Reciprocal Property of Pro…

The reciprocals of both sides of a proportion are also propor…

Properties of proportions

Similar figures

Similar polygons

Extended proportion

(1) a/b=c/d is = to b/a=d/c... (2) a/b=c/d is = to a/c=b/d... (3) a…

Have the same shape but not necessarily the same sides

If corresponding angles are congruent and if the length of co…

When 3 or more raitos set equal to eachother

Properties of proportions

(1) a/b=c/d is = to b/a=d/c... (2) a/b=c/d is = to a/c=b/d... (3) a…

Similar figures

Have the same shape but not necessarily the same sides