# Study sets matching "geometry chapter 9"

Study sets

Diagrams

Classes

Users

bases

bisect

circle

concentric circles

the congruent parallel polygons that form the "top" and "botto…

to divide into two congruent parts

the set of all points on a flat surface that are the same dist…

circles that have the same center

bases

the congruent parallel polygons that form the "top" and "botto…

bisect

to divide into two congruent parts

Transformation

Types of Transformation

Pre-Image

Image

Function of mapping that results in change in position, shape,…

Translation ... Reflection ... Rotation ... Dilation

Original image

Figure resulting from transformation of pre-image

Transformation

Function of mapping that results in change in position, shape,…

Types of Transformation

Translation ... Reflection ... Rotation ... Dilation

Angle of rotation

Axis of symmetry

Line of reflection

Line of symmetry

the angle through which a preimage is rotated to form the imag…

A line that divides a plane figure or a graph into two congrue…

A line that a figure is flipped across to create a mirror imag…

a line that divides a figure into two halves that are mirror i…

Angle of rotation

the angle through which a preimage is rotated to form the imag…

Axis of symmetry

A line that divides a plane figure or a graph into two congrue…

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Preimage

Image

Transformation

Rigid Transformation

the original figure in a transformation

The resulting figure after a transformation

A movement of a geometric figure

Movements of figures that preserve their shape and size

Preimage

the original figure in a transformation

Image

The resulting figure after a transformation

Transformation

Preimage

Image

Rigid motion

mapping or movement that results in a change of position, shap…

the original figure

The transformed, moved figure

a transformation that doesn't change distance between vertices…

Transformation

mapping or movement that results in a change of position, shap…

Preimage

the original figure

A transformation in which a second tran…

A transformation in which an original f…

Two figures where there is a sequence o…

A transformation in a plane that has a…

Composition of Transformations

Congruence Transformations (Isometry)

Congruent

Dilation

A transformation in which a second tran…

Composition of Transformations

A transformation in which an original f…

Congruence Transformations (Isometry)

Angle of rotation

Line of reflection

Line of symmetry

Rotational symmetry

the angle through which a preimage is rotated to form the imag…

A line that a figure is flipped across to create a mirror imag…

a line that divides a figure into two halves that are mirror i…

A figure can be rotated less than 360 degrees around a central…

Angle of rotation

the angle through which a preimage is rotated to form the imag…

Line of reflection

A line that a figure is flipped across to create a mirror imag…

transformation

reflection

isometry

line of symmetry

reflections, rotations, translations, and dilations are ALL tr…

a transformation that flips a figure. a figure can be reflecte…

also called a congruence transformation. means that the image…

if you fold a figure and the two halves match exactly, the fol…

transformation

reflections, rotations, translations, and dilations are ALL tr…

reflection

a transformation that flips a figure. a figure can be reflecte…

angle of depression

angle of elevation

cosine

geometric mean

The angle that a downward line of sight makes with a horizonta…

The angle that an upward line of sight makes with a horizontal…

The trigonometric ratio for acute angles that involves the len…

angle of depression

The angle that a downward line of sight makes with a horizonta…

angle of elevation

The angle that an upward line of sight makes with a horizontal…

A transformation in which a second tran…

A transformation in which an original f…

Two figures where there is a sequence o…

A transformation in a plane that has a…

Composition of Transformations

Congruence Transformations (Isometry)

Congruent

Dilation

A transformation in which a second tran…

Composition of Transformations

A transformation in which an original f…

Congruence Transformations (Isometry)

Pythagorean Triple

arithmetic mean

geometric mean

trigonometric ratio

three positive integers that satisfy the Pythagorean Theorem

add the numbers and divide

multiply the numbers and take the root

the ratio of two sides in a right triangle

Pythagorean Triple

three positive integers that satisfy the Pythagorean Theorem

arithmetic mean

add the numbers and divide

transformation

reflection

line of reflection

isometry

In a pane, a mapping for which each point has exactly one imag…

A transformation representing a flip of the figure over a poin…

A line through a figure that separates the figure into two mir…

A mapping for which the original figure and its image are cong…

transformation

In a pane, a mapping for which each point has exactly one imag…

reflection

A transformation representing a flip of the figure over a poin…

Pythagorean theorm

Converse of Pythagorean theorm

Pythagorean inequalities theorm

45-45-90 triangle theorm

In a right triangle- the square of the length of the hypotenus…

Is the square length of the longest side of a triangle is equa…

For any triangle ABC where c is the length of the longest side…

In a 45-45-90 triangle- they hypotenuse is √2 times as long as…

Pythagorean theorm

In a right triangle- the square of the length of the hypotenus…

Converse of Pythagorean theorm

Is the square length of the longest side of a triangle is equa…

Pythagorean theorem

Pythagorean triple

converse of the Pythagorean theorem

Pythagorean inequalities theorem

in a right triangle, the square of the length of the hypotenus…

is a set of three positive integers a, b, and that satisfy the…

if the square of the length of the longest side of a triangle…

for any triangle ABC, where c is the length of the longest sid…

Pythagorean theorem

in a right triangle, the square of the length of the hypotenus…

Pythagorean triple

is a set of three positive integers a, b, and that satisfy the…

Polygonal Region

Postulate 8 - The Area Postulate

Two facts about the area of a polygon

Number of feet in an acre

union of a polygon and its interior

The area of a polygon is always a positive number such that (1…

(1) congruent triangles have equal sides and (2) the area of a…

43,500 sq. ft.

Polygonal Region

union of a polygon and its interior

Postulate 8 - The Area Postulate

The area of a polygon is always a positive number such that (1…

transformation

reflection

isometry

line of symmetry

reflections, rotations, translations, and dilations are ALL tr…

a transformation that flips a figure. a figure can be reflecte…

also called a congruence transformation. means that the image…

if you fold a figure and the two halves match exactly, the fol…

transformation

reflections, rotations, translations, and dilations are ALL tr…

reflection

a transformation that flips a figure. a figure can be reflecte…

Transformation

Types of Transformation

Pre-Image

Image

Function of mapping that results in change in position, shape,…

Translation ... Reflection ... Rotation ... Dilation

Original image

Figure resulting from transformation of pre-image

Transformation

Function of mapping that results in change in position, shape,…

Types of Transformation

Translation ... Reflection ... Rotation ... Dilation

Transformation

Preimage

Image

Rigid Motion

Change the position, shape, or size of a figure.

Original figure in a transformation.

New figure after the transformation

A transformation that the figure maintains the same shape and…

Transformation

Change the position, shape, or size of a figure.

Preimage

Original figure in a transformation.

Center

Chord

Secant

Point of Tangency

given point from which all points on a circle are the same dis…

A segment whose endpoints are 2 points... on a circle.

A line that intersects a circle in two points

Point where a Tangent segment touches a circle

Center

given point from which all points on a circle are the same dis…

Chord

A segment whose endpoints are 2 points... on a circle.

State the pythagorean theorem:

What qualification do three side length…

30-60-90 triangle side relationships

45-45-90 triangle side relationships

the smallest two have to have a sum bigger than the biggest

State the pythagorean theorem:

What qualification do three side length…

the smallest two have to have a sum bigger than the biggest

Center

Chord

Secant

Point of Tangency

given point from which all points on a circle are the same dis…

A segment whose endpoints are 2 points... on a circle.

A line that intersects a circle in two points

Point where a Tangent segment touches a circle

Center

given point from which all points on a circle are the same dis…

Chord

A segment whose endpoints are 2 points... on a circle.

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transformation

preimage

image

isometry

change in geometric figures position, shape, or size

original figure before transformation - what you start with

resulting figure after transformation - what happens to it

when preimage and image are congruent but may be in different…

transformation

change in geometric figures position, shape, or size

preimage

original figure before transformation - what you start with

Pythagorean triple

Geometric mean

Trigonometric ratio

Tangent

Is a set of three positive integers a,b and c that satisfy the…

Of two positive numbers a and b is the positive number x that…

A ratio of the lengths of two sides in a right triangle

Ratio is a trigonometric ratio for acute angles that involves…

Pythagorean triple

Is a set of three positive integers a,b and c that satisfy the…

Geometric mean

Of two positive numbers a and b is the positive number x that…

transformation

preimage

image

translation

an action that changes the position, shape, or size of a figure

the original figure (before a transformation)

the resulting figure (after a transformation)

an action that moves all the points in a figure a specific dis…

transformation

an action that changes the position, shape, or size of a figure

preimage

the original figure (before a transformation)

Pythagorean Theorem

Converse of Pythagorean Theorem

Isosceles Right Triangle

30-60-90 Right Triangle

Hypotenuse^2 = Leg^2 * Leg^2

If the three sides match the theorem, its a right triangle

Hypotenuse= leg*squarerootoftwo

Pythagorean Theorem

Hypotenuse^2 = Leg^2 * Leg^2

Converse of Pythagorean Theorem

If the three sides match the theorem, its a right triangle