# Study sets matching "geometry chapter 6 similarity"

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ratio

proportion

cross multiplication

properties of similar polygons

for any two numbers (x and y), it is the quotient you get by d…

an equation stating that two ratios are equal... x:y = a:b

a way to determine a variable in a proportion ... ex: 6:x = 5:15…

- corresponding angles are congruent... - corresponding sides are…

ratio

for any two numbers (x and y), it is the quotient you get by d…

proportion

an equation stating that two ratios are equal... x:y = a:b

Similar Polygons

scale factor

Perimeters of Similar Polygons

Angle-Angle (AA) Similarity Postulate

Two polygons whose corresponding angles are congruent and whos…

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

If two polygons are similar, then their perimeters are proport…

If two corresponding angles of two or more triangles are congr…

Similar Polygons

Two polygons whose corresponding angles are congruent and whos…

scale factor

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

center of dilation

dilation

enlargement

extremes

in a dilation, the fixed point about which a figure is enlarge…

a transformation that stretches or shrinks a figure to create…

dilation with a scale factor greater than 1

the first and last term of a proportion

center of dilation

in a dilation, the fixed point about which a figure is enlarge…

dilation

a transformation that stretches or shrinks a figure to create…

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6.1: Use Similar Polygons

Problem 1

Problem 2

6.3: Prove Triangles Similar by AA

a) Show that the polygons are similar.... b) Write a similarity s…

a) Show that the polygons are similar.... b) Write a similarity s…

6.1: Use Similar Polygons

Problem 1

a) Show that the polygons are similar.... b) Write a similarity s…

ratio

proportion

similar

scale factor

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

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 fir…

proportion

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

Geometric Mean

How do you know if points form a segmen…

Similar polygons

Scale factor

Its of 2 positive numbers ... And can look like this ... 2/GM=GM/8

It is a segment if the slopes are the same.... It is a triangle i…

They have congruent angles and side lengths are proportional…

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

Geometric Mean

Its of 2 positive numbers ... And can look like this ... 2/GM=GM/8

How do you know if points form a segmen…

It is a segment if the slopes are the same.... It is a triangle i…

Dilation

contraction

expansion

scale factor

a transformation that produces an image that is the same shape…

reduction (a number between zero and one)

enlargement (the scale factor is larger than one)

k= image / preimage

Dilation

a transformation that produces an image that is the same shape…

contraction

reduction (a number between zero and one)

Definition of Similar Figures

Scale Factor

AA similarity

SAS Similarity Theorem

Two figures are similar if: ... (1) Their corresponding angles a…

the ratio of the lengths of two corresponding sides

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

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

Definition of Similar Figures

Two figures are similar if: ... (1) Their corresponding angles a…

Scale Factor

the ratio of the lengths of two corresponding sides

similar

scale factor

dilation

AA similarity postulate

same shape, different size

the ratio of the lengths of two corresponding sides

a transformation that preserves angle measure and results in a…

if two angles of one triangle are congruent to two angles of a…

similar

same shape, different size

scale factor

the ratio of the lengths of two corresponding sides

ratio

proportion

means of a proportion

extremes of a proportion

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

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 dif…

proportion

An equation stating that two ratios are equal

Sine

Cosine

Tangent

Adjacent Leg

The trigonometric function that is equal to the ratio of the s…

The trigonometric function that is equal to the ratio of the s…

The trigonometric function that is equal to the ratio of the o…

Is adjacent to the theta angle.

Sine

The trigonometric function that is equal to the ratio of the s…

Cosine

The trigonometric function that is equal to the ratio of the s…

two polygons are similar polygons if

if 2 polygons are similar than the rati…

perimeters of similar triangles (theore…

similarity of congruence

corresponding angels are congruent and side lengths are propor…

scale factor

if 2 polygons are similar, then the ratio of their perimeters…

notice that if any two congruent figures are also similar, you…

two polygons are similar polygons if

corresponding angels are congruent and side lengths are propor…

if 2 polygons are similar than the rati…

scale factor

Scale Factor

AA Similarity

SAS Similarity

SSS Similarity

The ratio of any two corresponding lengths in two similar geom…

two pairs of angles of triangles are congruent = similar

If an angle of 1 triangle is congruent to an angle of a second…

If the measures of the corresponding sides of two triangles ar…

Scale Factor

The ratio of any two corresponding lengths in two similar geom…

AA Similarity

two pairs of angles of triangles are congruent = similar

Scale Drawing

Scale

Proportion

Similar Polygons

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

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

Two ratios that are equal

A set of polygons where corresponding angles are congruent and…

Scale Drawing

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

Scale

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

Ratios

Proportions

Geometric Mean

Altitude Rule Right Triangle

An order pair of numbers, proportions... compare one part of the…

An equation stating that two ratios are equal.

For any positive numbers a and b, the positive number x such t…

The Geometric Mean is the altitude of a right triangle

Ratios

An order pair of numbers, proportions... compare one part of the…

Proportions

An equation stating that two ratios are equal.

Ratio

Extended ratios

Proportions

Cross product property

A comparison of two quantities using division

Used to complete 3 or more quantities a:b:c

Equation stating two ratios are equal

The product of the extremes equals the product of the means ... A…

Ratio

A comparison of two quantities using division

Extended ratios

Used to complete 3 or more quantities a:b:c

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Ratio

Extended Ratio

Proportion

Scale Drawings

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

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

An equation stating that two ratios are equal.

A drawing that shows a real object with accurate proportions r…

Ratio

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

Extended Ratio

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

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

congruent figures

congruence transformation

dilation

scale factor

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

rigid motion

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

the ratio of the corresponding sides in a dilation

congruent figures

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

congruence transformation

rigid motion