How can we help?

You can also find more resources in our Help Center.

Similar Polygons

Scale Factor

Two polygons are similar if the corres…

Two polygons are similar if the corres…

2 Polygons are similar if corresponding angles are congruent…

If 2 polygons are similar, then the ratio of the lengths of t…

Congruent

Similar

Similar Polygons

2 Polygons are similar if corresponding angles are congruent…

Scale Factor

If 2 polygons are similar, then the ratio of the lengths of t…

Ratio

Proportion

Similar polygons

Scale Factor

a comparison of 2 quantities

equation stating that 2 ratios are equal, solved by cross-mul…

polygons that are the same shape, but different sizes

ratio comparing the lengths of corresponding sizes of similar…

Ratio

a comparison of 2 quantities

Proportion

equation stating that 2 ratios are equal, solved by cross-mul…

Ratio

Proportion

Similar Polygons

Scale Factor

A comparison of two quantities

Equation stating that two ratios are equal. You solve a propo…

Polygons that are the same shape but different sizes

Ratio comparing the lengths of corresponding sides of similar…

Ratio

A comparison of two quantities

Proportion

Equation stating that two ratios are equal. You solve a propo…

Proportion

Means

Extremes

Geometric Mean

An equation that states that two ratios are equal

In a proportion, the denominator of the first equation and th…

In a proportion, the numerator of the first equation and the…

A positive number that satisfies the proportion a/x= x/b; x =…

Proportion

An equation that states that two ratios are equal

Means

In a proportion, the denominator of the first equation and th…

Proportion

Means

Extremes

Geometric Mean

An equation that states that two ratios are equal

In a proportion, the denominator of the first equation and th…

In a proportion, the numerator of the first equation and the…

A positive number that satisfies the proportion a/x= x/b; x =…

Proportion

An equation that states that two ratios are equal

Means

In a proportion, the denominator of the first equation and th…

Proportion

Means

Extremes

Scale Factor

An equation that states that two ratios are equal

In a proportion, the denominator of the first equation and th…

In a proportion, the numerator of the first equation and the…

The common ratio of the lengths of two corresponding sides of…

Proportion

An equation that states that two ratios are equal

Means

In a proportion, the denominator of the first equation and th…

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…

Proportion

Means

Extremes

Geometric Mean

An equation that states that two ratios are equal

In a proportion, the denominator of the first equation and th…

In a proportion, the numerator of the first equation and the…

A positive number that satisfies the proportion a/x= x/b; x =…

Proportion

An equation that states that two ratios are equal

Means

In a proportion, the denominator of the first equation and th…

Proportion

Means

Extremes

Geometric Mean

An equation that states that two ratios are equal

In a proportion, the denominator of the first equation and th…

In a proportion, the numerator of the first equation and the…

A positive number that satisfies the proportion a/x= x/b; x =…

Proportion

An equation that states that two ratios are equal

Means

In a proportion, the denominator of the first equation and th…

Proportion

Means

Extremes

Geometric Mean

An equation that states that two ratios are equal

In a proportion, the denominator of the first equation and th…

In a proportion, the numerator of the first equation and the…

A positive number that satisfies the proportion a/x= x/b; x =…

Proportion

An equation that states that two ratios are equal

Means

In a proportion, the denominator of the first equation and th…

Ratio

Extended ratios

Proportion

Means

The comparison of two numbers using division; the ratio of a…

Ratios that compare more than 2 values; example: ratios of th…

An equation that states that two ratios are equal

In a proportion, the denominator of the first equation and th…

Ratio

The comparison of two numbers using division; the ratio of a…

Extended ratios

Ratios that compare more than 2 values; example: ratios of th…

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

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

geometric mean

scale

a comparison if two numbers using division

an equation that states that two ratios are equal

for two positive number (a & B) the positive number x that sa…

a ratio that describes how the dimensions in a scale drawing…

ratio

a comparison if two numbers using division

proportion

an equation that states that two ratios are equal

Scale Drawing

Scale

Proportion

Similar Polygons

a drawing that is the same shape as the object it represents…

A ratio that describes how the dimensions in the drawing are…

Two ratios that are equal

A set of polygons where corresponding angles are congruent an…

Scale Drawing

a drawing that is the same shape as the object it represents…

Scale

A ratio that describes how the dimensions in the drawing are…

Reciprocal Property

perimeters of similar polygons

Angle-Angle Similarity Postulate

Side Side Side Similarity Theorem

If two ratios are equal, then their reciprocals are also equal

if two polygons are similar, them the ratio of their perimete…

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

If the corresponding side lengths of two triangles are propor…

Reciprocal Property

If two ratios are equal, then their reciprocals are also equal

perimeters of similar polygons

if two polygons are similar, them the ratio of their perimete…

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

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)

Proportion

What values are the extremes and means?

Cross product property

Geometric mean

Equation states 2 ratios are equal

a & d extremes whereas c & b are means

product extremes = product means

x = square root ab and a/x = x/b

Proportion

Equation states 2 ratios are equal

What values are the extremes and means?

a & d extremes whereas c & b are means

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…

Ratio

Extended Ratio

Proportion

Scale Drawings

A comparison of two or more quantities written as a/b, a:b, o…

A comparison of three or more quantities written as a:b:c or…

An equation stating that two ratios are equal.

A drawing that shows a real object with accurate proportions…

Ratio

A comparison of two or more quantities written as a/b, a:b, o…

Extended Ratio

A comparison of three or more quantities written as a:b:c or…

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

Ratio

Extended Ratios

Proportion

Extremes and Means

A comparison of two quantities using division.... Ex. a:b

Used to compare three or more quantities.... Ex. a:b:c

An equation stating that two ratios are equal.

Ratio

A comparison of two quantities using division.... Ex. a:b

Extended Ratios

Used to compare three or more quantities.... Ex. a:b:c

What makes polygons similar?

Geometric Mean

Name the 4 Triplets.

What are the three ways to prove simil…

corresponding angles & proportional sides

between a and b is square root of ab. (square root of their p…

(3,4,5), (8,15,17), (5,12,13), (7,24,25)

AA similarity, SSS similarity, SAS similarity

What makes polygons similar?

corresponding angles & proportional sides

Geometric Mean

between a and b is square root of ab. (square root of their p…

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…

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

AA Similarity Postulate

SAS Similarity Postulate

SSS Similarity Postulate

Triangle Proportionality Theorem

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

If an angle of one triangle is congruent to an angle of a sec…

If the corresponding sides of two triangles are proportional,…

If a line is parallel to one side of a triangle and intersect…

AA Similarity Postulate

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

SAS Similarity Postulate

If an angle of one triangle is congruent to an angle of a sec…

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

a:b = c:d which is means and which is…

geometric mean

golden ratio or golden mean

def similar

means: b and c... extremes: a and d

a/x = x/d ad = x^2

...

- corr angles are congruent... - lengths of corr sides are propo…

a:b = c:d which is means and which is…

means: b and c... extremes: a and d

geometric mean

a/x = x/d ad = x^2

Similar (11.1)

Dilation (11.1)

Scale Factor (11.1)

Dilation Similarity Conjecture (11.1)

Identical in shape but not necessarily in size. Two figures a…

A non-rigid transformation that enlarges or reduces a geometr…

The ratio of corresponding lengths in similar figures.

If one polygon is a dilated image of another polygon, then th…

Similar (11.1)

Identical in shape but not necessarily in size. Two figures a…

Dilation (11.1)

A non-rigid transformation that enlarges or reduces a geometr…

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…

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…

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

similarity

similar figures

proportion

property of proportions

two geometric figures are similar if they have the exact same…

figures whose corresponding angles are congruent and correspo…

two ratios [fractions] that are equal ... Given: (x/y)=(a/b) the…

Given: (AB/CD)=(BD/AC) , then ABxAC=BDxCD or (AB/BD)=(CD/AC )…

similarity

two geometric figures are similar if they have the exact same…

similar figures

figures whose corresponding angles are congruent and correspo…

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…

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…

what is a ratio

Proportion

Geometric means

a/b=c/d

a comparison of 2 numbers. ... Ex: a:b, a/b, a to b

An equation that sets 2 ratios equal. ... Ex: a/b = c/d... b,c are…

a proportion where the means are the same.... Ex: a/b=b/d

ad=bc... a/c=b/d... b/a=d/c... a+b/b=c+d/d

what is a ratio

a comparison of 2 numbers. ... Ex: a:b, a/b, a to b

Proportion

An equation that sets 2 ratios equal. ... Ex: a/b = c/d... b,c are…

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

congruent figures

congruence transformation

dilation

scale factor

same size and shape; can be mapped onto each other with a ser…

rigid motion

a transformation where a figure is mapped onto itself with en…

the ratio of the corresponding sides in a dilation

congruent figures

same size and shape; can be mapped onto each other with a ser…

congruence transformation

rigid motion

base angles of a trapezoid

consecutive angles

isosceles trapezoid

kite

each pair of adjacent angles to a base

share a common side

whose nonparallel opposite sides are congruent.

is a quadrilateral with two pairs of congruent adjacent sides…

base angles of a trapezoid

each pair of adjacent angles to a base

consecutive angles

share a common side

Ratio

Extended Ratio

Proportion

Extremes

A comparison of two quantities by division ... a/b, a:b, a to b…

A comparison of three numbers. There are three ratios in an _…

An equation that states that two ratios are equal.

The numerator of the first ratio in a proportion and the deno…

Ratio

A comparison of two quantities by division ... a/b, a:b, a to b…

Extended Ratio

A comparison of three numbers. There are three ratios in an _…