# Study sets matching "geometry chapter 7 similar polygons"

Ratio

To find the ratio of the lengths of two…

Proportion

Extremes

The quotient when the first number is divided by the second... -T…

Measured in the same units

An equation stating that two ratios are equal

First & last terms of a proportion

Ratio

The quotient when the first number is divided by the second... -T…

To find the ratio of the lengths of two…

Measured in the same units

ratio

quotient is usually expressed in ...

there are ... units in a ratio

to find the ratio of the lengths of two…

the quotient when a number is divided by another

simplest form

NO

the segments must be measured in terms of the same unit

ratio

the quotient when a number is divided by another

quotient is usually expressed in ...

simplest form

Ratio

Proportions

Means extreme property

Similar polygons

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

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 i…

Proportions

Is an equation stating that two ratios are equal.

Ratio

To find the ratio of the lengths of two…

Proportion

Extremes

The quotient when the first number is divided by the second... -T…

Measured in the same units

An equation stating that two ratios are equal

First & last terms of a proportion

Ratio

The quotient when the first number is divided by the second... -T…

To find the ratio of the lengths of two…

Measured in the same units

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.

MEPP - Means-Extremes Property of Propo…

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 Propo…

the product of the extremes equals the product of the means

Property of Proportions A

a/b=c/d = ad=bc

AA similarity

SAS similarity

No

SSS similarity

How are these triangles similar?

How are these triangles similar?

Are these triangles similar?

How are these triangles similar?

AA similarity

How are these triangles similar?

SAS similarity

How are these triangles similar?

King Henry Died Unexpectedly Drinking C…

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 C…

Kilo Hecto Deca Unit Deci Centi Milli

Extremes

First and last terms of proportion

If two polygons are similar, their vert…

If two angles of one triangle are congr…

If an angle of one triangle is congruen…

If the sides of two triangles are in pr…

1. congruent... 2. in proportion

...the triangles are similar

...the triangles are similar

...the triangles are similar

If two polygons are similar, their vert…

1. congruent... 2. in proportion

If two angles of one triangle are congr…

...the triangles are similar

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 sides…

in the same ratio

Proportion

an equation stating that two ratios are equal

Similar polygons

figures that have the same shape but different size

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

proportion

extremes

means

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

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 to…

proportion

eq stating that two ratios are =

SAS Similarity Theorem. If an angle of…

SSS Similarity Theorem. If the sides of…

Triangle Proportionality Theorem. If a…

If three parallel lines intersect two t…

then the triangles are similar

then the triangles are similar

then it divides those sides proportionally

then they divide the transversals proportionally

SAS Similarity Theorem. If an angle of…

then the triangles are similar

SSS Similarity Theorem. If the sides of…

then the triangles are similar

Ratio

Unit ratio

Proportion

Means and extremes

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

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... usuall…

Unit ratio

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

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 lengt…

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 statement…

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

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…

Means-extremes Property

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

A Property of Proportions

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

Ratio- the ratio of one to another is t…

Proportion- an equation stating that 2…

Extremes- the first and last terms of a…

Means- the middle terms of a proportion

Ratio of 8 to 12 is 2/3 or 2:3

a/b=c/d and a:b=c:d... a, b, c, d are terms of the proportion... ext…

a:b=c:d... "a" and "d" are extremes

a:b=c:d... "b" and "c" are means

Ratio- the ratio of one to another is t…

Ratio of 8 to 12 is 2/3 or 2:3

Proportion- an equation stating that 2…

a/b=c/d and a:b=c:d... a, b, c, d are terms of the proportion... ext…

Ratio

Proportion

Extremes

A,d

The quotient when the first number is divided by the second. U…

An equation stating that two ratios are equal: a/b = c/d

First and last terms in a proportion (a,d)

The extremes are

Ratio

The quotient when the first number is divided by the second. U…

Proportion

An equation stating that two ratios are equal: a/b = c/d

Postulate AAA

Theorem 59 (Page 327)

Theorem 60 (Page 327)

Theorem 61 (Page 334)

If there exists a correspondence between the vertices of two t…

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

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

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

Postulate AAA

If there exists a correspondence between the vertices of two t…

Theorem 59 (Page 327)

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

When are two polygons similar?

Find the scale factor of the ratio of t…

what is the similarity of two polygons…

is the scale factor of these polygons s…

when their corresponding angles are congruent and side lengths…

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 ... 18/36…

yes ... 0.4

When are two polygons similar?

when their corresponding angles are congruent and side lengths…

Find the scale factor of the ratio of t…

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

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.…

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