# Study sets matching "geometry chapter 9"

Study sets

Diagrams

Classes

Users

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

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

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

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…

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)

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)

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…

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

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…

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.

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.

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.

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

isometry

reflections

reflections across the x-axis

reflections across the y-axis

is a transformation that does not change the shape or size of…

a reflection is a transformation across a line, called the lin…

(x,y) goes to (x,-y)

(x,y) goes to (-x,y)

isometry

is a transformation that does not change the shape or size of…

reflections

a reflection is a transformation across a line, called the lin…

Angle of rotation

Center of rotation

Composition of transformations

Glide reflection

An angle through with a preimage is rotated to form an image.

A fixed point which shapes move in a circular motion to a new…

When a transformation is applied to a figure and then another…

The composition of a TRANSLATION followed by a REFLECTION in a…

Angle of rotation

An angle through with a preimage is rotated to form an image.

Center of rotation

A fixed point which shapes move in a circular motion to a new…

Pythagoras and Converse Theorem

Pythagoras Triples

Geometric Means

Special Triangles - 3-60-90

a^2+b^2=c^2... c^2____a^2+b^2... = is right... less = acute... more = obtu…

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

appearance twice, once in the numerator and one in the denomin…

Pythagoras and Converse Theorem

a^2+b^2=c^2... c^2____a^2+b^2... = is right... less = acute... more = obtu…

Pythagoras Triples

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

The Pythagorean Theorem

if a squared + b squared is greater tha…

If a squared + b squared is less than c…

If a squared plus b squared equals c sq…

In a right triangle only, the sum of the squares of the legs e…

the triangle is acute

the triangle is obtuse

the triangle is right.

The Pythagorean Theorem

In a right triangle only, the sum of the squares of the legs e…

if a squared + b squared is greater tha…

the triangle is acute