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Study sets matching "geometry chapter 7 similar polygons"

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Study sets matching "geometry chapter 7 similar polygons"

11 terms
Geometry Chapter 7 Similar Polygons
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…
14 terms
Chapter 7 Geometry- Similar Polygons
Ratio
Proportion
Extremes
Means
First number divided by the second
Equation stating that two ratios are equal
First and last terms of a proportion
Middle terms of a proportion
Ratio
First number divided by the second
Proportion
Equation stating that two ratios are equal
10 terms
Geometry: Chapter 7 Similar Polygons
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.
14 terms
Chapter 7-Similar Polygons
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
14 terms
10 Geometry Chapter 7 Similar Polygons Terms
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
10 terms
Chapter 7 Similar Polygons
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
11 terms
Chapter 7: Similar Polygons
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 =
40 terms
7 Geometry Similar Polygons
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.
9 terms
Chapter 7: Similar Polygons
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
10 terms
Chapter 7: Similar Polygons
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
9 terms
Chapter 7 - Similar Polygons
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…
8 terms
Chapter 7 Similar Polygons
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
9 terms
Geometry Chapter 7: Ratios and Proportions, Similar Polygons, Similar Triangles, and Similar Right Triangles
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.
8 terms
Chapter 7: Similar Polygons
Ratio
Simplest ratio
Proportion
Cross multiplication: a/b = c/d
Compares two numbers
Reduced ratio
Equation that relates two ratios
ad = bc
Ratio
Compares two numbers
Simplest ratio
Reduced ratio
10 terms
Chapter 7, Similar Polygons
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…
14 terms
Chapter 7- Similar Polygons
The ratio of 8 to 12
What does 8/12 simplify to?
A poster is 8 ft high and 12 inches wi…
The ratio of the measures of the angle…
8:12 or 8/12
2/3
1/8
40, 40, and 100.
The ratio of 8 to 12
8:12 or 8/12
What does 8/12 simplify to?
2/3
10 terms
Geometry Chapter 7 Similarity
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…
23 terms
Geometry Ch. 7 Similar polygons
always
sometimes
sometimes
sometimes
two equilateral triangles
two right triangles
two isosceles triangles
two scalene triangles
always
two equilateral triangles
sometimes
two right triangles
11 terms
Geometry Chapter 7 Similarity
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…
10 terms
Geometry 7-2 Similar Polygons
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…
18 terms
Chapter 7: Similar Polygons (Test)
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
11 terms
Geometry Chapter 7 - Similarity
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
14 terms
Geometry Chapter 7 - Similarity
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
9 terms
Geometry - Chapter 5 - Similar Polygons and the Pythagorean Theorem
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.
22 terms
Geometry - Chapter 7 - Similarity
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)
12 terms
The geometry of polygons (chapter 7)
Revolution
Straight angle
Right angle
Acute angle
One complete turn = 360°
1/2 turn = 180°
1/4 turn = 90°
Less than a 1/4 turn = Between 0° to 90°
Revolution
One complete turn = 360°
Straight angle
1/2 turn = 180°
13 terms
Chapter 7 Similarity Geometry
Ratio
Proportion
Extremes
Means
Compares two numbers by division
Is an equation stating that two ratios are equal
the values a and d,
the values b and c, in the proportion a/b=c/d
Ratio
Compares two numbers by division
Proportion
Is an equation stating that two ratios are equal
20 terms
Geometry-Chapter 7- Similarity
Distance Formula
Midpoint Formula
Golden Ratio
Golden Rectangle
√(x₁-x₂)² + (y₁-y₂)²
(x₁+x₂÷2, y₁+y₂÷2)
1.618 : 1
a rectangle that can be divided into a square and rectangle s…
Distance Formula
√(x₁-x₂)² + (y₁-y₂)²
Midpoint Formula
(x₁+x₂÷2, y₁+y₂÷2)
11 terms
Geometry-Chapter 7-Similarity
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
Geometry: chapter 7- similarity
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
10 terms
Geometry Chapter 7 Similarity
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…
10 terms
Geometry for Enjoyment & Challenge: Chapter 8 Similar Polygons
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…
9 terms
Geometry-Chapter 7- Similarity
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…
24 terms
Geometry Chapter 7 - Similarity
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
39 terms
Geometry Chapter 7: Quadrilaterals and Other Polygons
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-…
10 terms
Geometry for Enjoyment & Challenge: Chapter 8 Similar Polygons
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…
10 terms
Geometry Chapter 7 Similarity
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…
9 terms
Geometry Chapter 7: Similarity Vocabulary
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…
Similarity (Geometry) Chapter 7
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
10 terms
Chapter 7 Similarity ( Geometry)
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…
24 terms
Geometry Unit 7: Similar Polygons, Trigonometry, Areas of Polygons
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
5 terms
7.2 Similar Polygons
Answer #1:... Yes they are similar. The s…
Answer #2: B
Answer #3: No they are not similar.
Answer #4: x = 6
Question #1:
Question #2:
Question #3:
Question #4:
Answer #1:... Yes they are similar. The s…
Question #1:
Answer #2: B
Question #2:
12 terms
Geometry Chapter 7 - Similarity
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
12 terms
Geometry Chapter 7: Similarity
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…
20 terms
Geometry for Enjoyment & Challenge: Chapter 7 Polygons
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…
10 terms
Chapter 7 Geometry Similarity & Trigonometry Vocabulary
Sine
Cosine
Tangent
Adjacent Leg
= Opposite / Hypotenuse
is adjacent next to the theta angle
Sine
= Opposite / Hypotenuse
Cosine
14 terms
Geometry chapter 7 similarity vocab
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
6 terms
7-2 Similar Polygons
Similar polygons
Similar mark
2 similar polygons
Similarity ratio
Same shape diff size
~
Corresponding sides proportional... Corresponding angles congruent
Bigger or smaller than actual size
Similar polygons
Same shape diff size
Similar mark
~
21 terms
Geometry - Chapter 5 - Similar Polygons and the Pythagorean Theorem & Postulates
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…
14 terms
Geometry chapter 7 similarity vocab
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
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