#### Study sets matching "geometry chapter 9"

#### Study sets matching "geometry chapter 9"

bases

bisect

circle

concentric circles

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

to divide into two congruent parts

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

circles that have the same center

bases

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

bisect

to divide into two congruent parts

transformation

reflection

isometry

line of symmetry

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

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

also called a congruence transformation. means that the image…

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

transformation

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

reflection

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

Angle of rotation

Axis of symmetry

Line of reflection

Line of symmetry

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

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

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

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

Angle of rotation

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

Axis of symmetry

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

transformation

isometry

translation

preimage

A change in the position, shape, or size of a figure.

A transformation in which the preimage and image are congruent

All points in a figure move the same distance in the same dir…

The given or original figure on which a transformation is per…

transformation

A change in the position, shape, or size of a figure.

isometry

A transformation in which the preimage and image are congruent

transformation

preimage

image

isometry

a change in the position, shape, or size of a figure

the original figure

the transformed figure

a transformation in which the preimage and image are congruent

transformation

a change in the position, shape, or size of a figure

preimage

the original figure

Center

Chord

Secant

Point of Tangency

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

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 di…

Chord

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

bases

bisect

circle

concentric circles

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

to divide into two congruent parts

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

circles that have the same center

bases

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

bisect

to divide into two congruent parts

transformation

reflection

line of reflection

isometry

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

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

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

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

transformation

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

reflection

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

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.

circle

center

radius

chord

the set of points in a plane that are a given distance from a…

the given point at the middle of the circle

the distance from the center to the edge of the circle

a segment whose endpoints lie on a circle

circle

the set of points in a plane that are a given distance from a…

center

the given point at the middle of the circle

Line of Reflection

Translation Vector

Center of Rotation

Angle of Rotation

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

The vector in which a translation maps each point to its image

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

The angle through which a preimage is rotated to form the image

Line of Reflection

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

Translation Vector

The vector in which a translation maps each point to its image

angle of depression

angle of elevation

cosine

inverse cosine

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

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

Adjacent over hypotenuse.

An inverse trig ratio that lets you go backwards to find the…

angle of depression

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

angle of elevation

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

preimage

component form

image

transformation

the original figure before it is manipulated

horizontal first, then vertical

the new figure after it has been manipulated

manipulation that changes a figure

preimage

the original figure before it is manipulated

component form

horizontal first, then vertical

Alternate Interior Angles

Exterior Angle

Complementary Angles

Supplementary Angles

Angles between a pair of lines that switch sides of a third i…

When a side of a triangle is extended to form an angle outsid…

Two angles whose measures add up to 90°. Angles T and V are c…

Two angles whose measures add up to 180°. Angles A and B are…

Alternate Interior Angles

Angles between a pair of lines that switch sides of a third i…

Exterior Angle

When a side of a triangle is extended to form an angle outsid…

Ratio

Proportion

Cross Products

Geometric Mean

A comparison of two quantities

An equation that states that two ratios are equal

In a proportion, if a/b=c/d, then a

**d = b**aIn a proportion, If a/b = x/b, the geometric mean ... of a and b…

Ratio

A comparison of two quantities

Proportion

An equation that states that two ratios are equal

15

9.2

40

170

The perimeter of a rectangle with length of 5cm and width of…

The perimeter of a square with sides of length 2.3mm is _____…

The perimeter of a parallelogram with two sides 12cm long and…

The perimeter of a regular pentagon with sides of length 34in…

15

The perimeter of a rectangle with length of 5cm and width of…

9.2

The perimeter of a square with sides of length 2.3mm is _____…

radius

chord

diameter

secant

a segment that joins the center to a point on the circle

segments whose endpoints lie on the circle

a chord that contains the center

contains a chord; extends beyond the circle points

radius

a segment that joins the center to a point on the circle

chord

segments whose endpoints lie on the circle

point

line

plane

coplanar lines

A location in space with no size or shape. Represented by a d…

A straight continuous arrangement of an infinite number of po…

A flat surface with infinite length and width, but no depth.…

Two or more lines located in one plane.

point

A location in space with no size or shape. Represented by a d…

line

A straight continuous arrangement of an infinite number of po…

Transformation

Reflection

Rotation

Translation

A figure that has the same shape but is rotated, flipped, dil…

Mirror Image of a figure

one point rotating on a specific point by a given angle.

Sliding or Moving a shape but without rotating or flipping th…

Transformation

A figure that has the same shape but is rotated, flipped, dil…

Reflection

Mirror Image of a figure

Postulate 8 or The Area Postulate

Postulate 9

Corollary to Postulate 9

Theorem 38

Every polygonal region has a positive number called its area…

The area of a rectangle is the product of its base and altitu…

The area of a square is the square of its sides.

The area of a right triangle is half the product of its legs.

Postulate 8 or The Area Postulate

Every polygonal region has a positive number called its area…

Postulate 9

The area of a rectangle is the product of its base and altitu…

transformation

preimage

image

isometry

a change in position, shape or size of a geometric figure

the original figure

the resulting figure

a transformation in which the preimage and image are congruent

transformation

a change in position, shape or size of a geometric figure

preimage

the original figure

Theorem 9.1

Theorem 9.2

Theorem 9.3

Theorem 9.5 Converse of the Pythagorea…

If the altitude is drawn to the hypotenuse of a right triangl…

In a right triangle, the altitude from the right angle to the…

In a right triangle, the altitude from the right angle to the…

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

Theorem 9.1

If the altitude is drawn to the hypotenuse of a right triangl…

Theorem 9.2

In a right triangle, the altitude from the right angle to the…

glide reflection

reduction

rotational symmetry

isometry

A composition of a glide (translation and a reflection in a l…

When the scale factor is between 0 and 1 between the preimage…

A figure has this if it is its own image for some rotation.

A type of transformation in which the preimage and image are…

glide reflection

A composition of a glide (translation and a reflection in a l…

reduction

When the scale factor is between 0 and 1 between the preimage…

transformation

reflection

rotation

image

moves or changes a figure in some way to produce a new figure

a transformation that uses a line like a mirror to reflect an…

a transformation in which a figure is turned about a fixed po…

the new figure that a transformation produces

transformation

moves or changes a figure in some way to produce a new figure

reflection

a transformation that uses a line like a mirror to reflect an…

angle of rotation

angle of rotational symmetry

center of dilation

center of rotation

an angle formed by a rotating ray, called the terminal side,…

The smallest angle through which a figure with rotational sym…

The intersection of the lines that connect each point of the…

The point around which a figure is rotated.

angle of rotation

an angle formed by a rotating ray, called the terminal side,…

angle of rotational symmetry

The smallest angle through which a figure with rotational sym…

Transformation

Preimage

Image

Rigid Motion

A change in position, size, or shape of a geometric figure.

Original figure before a transformation. (Ex. Triangle ABC)

Resulting figure after a transformation. (Ex. Triangle A'B'C')

Transformation in the plane that preserves distance and angle…

Transformation

A change in position, size, or shape of a geometric figure.

Preimage

Original figure before a transformation. (Ex. Triangle ABC)

Transformation

Rigid or Congruence Transformation

Examples of Rigid Transformation

Non-Rigid or Similarity Transformation

changes the orientation, location, and size of a figure

a transformation where the figure maintains its shape and size

reflection, translation, rotation

a transformation where the figure maintains its shape but not…

Transformation

changes the orientation, location, and size of a figure

Rigid or Congruence Transformation

a transformation where the figure maintains its shape and size

point

line

plane

coplanar line

A location in space that has no size or shape. Often represen…

A straight continuous arrangement of an infinite number of po…

A flat surface that extends infinitely in all directions. Has…

Two or more lines that are located in the same plane.

point

A location in space that has no size or shape. Often represen…

line

A straight continuous arrangement of an infinite number of po…

circle

center

radius

fact

the set of points in a plane equidistant from a fixed point

fixed point in a circle

distance from the center to a point on a circle

all radii are congruent in the same circle

circle

the set of points in a plane equidistant from a fixed point

center

fixed point in a circle

image

preimage

isometry

vector

the product of a transformation, a new figure

the original figure

a transformation that preserves length and angle measure

a quantity that has both directions and magnitude, or size

image

the product of a transformation, a new figure

preimage

the original figure

apothem

central angle

circle

area

perpendicular distance from the center of a regular polygon t…

angle whose vertex is the center of the circle

set of points in a plane that are a fixed distance from a giv…

The number of square units required to cover a surface.

apothem

perpendicular distance from the center of a regular polygon t…

central angle

angle whose vertex is the center of the circle

circle

radius

chord

diameter

round plane figure whose boundary (the circumference) consist…

straight line from the center to the circumference of a circl…

a geometric line segment whose endpoints both lie on the circle

straight line passing from side to side through the center of…

circle

round plane figure whose boundary (the circumference) consist…

radius

straight line from the center to the circumference of a circl…

Transformation

Isometry

Translation

Translation along <a,b>

Moves or changes a figure in some way to produce a new figure…

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

Transformation along a vector

(x, y) --> (x + a, y + b)

Transformation

Moves or changes a figure in some way to produce a new figure…

Isometry

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

Apothem

Center of a Circle

Center of a regular polygon

Central angle of a regular polygon

perpendicular distance from the center of a regular polygon t…

point inside a circle that is the same distance from every po…

point that is equidistant from all vertices of the regular po…

angle whose vertex is the center of the regular polygon, and…

Apothem

perpendicular distance from the center of a regular polygon t…

Center of a Circle

point inside a circle that is the same distance from every po…

a tangent to a circle is_____ the radi…

tangent segments to a circle from a po…

if two chords in a circle are congruen…

if two chords in a circle are congruen…

perpendicular

congruent

congruent

arcs

a tangent to a circle is_____ the radi…

perpendicular

tangent segments to a circle from a po…

congruent

cone

face

edge

polyhedron

a three-dimensional figure with one vertex and one circular b…

a flat surface of a polyhedron

the line segment along which two faces of a polyhedron inters…

a three-dimensional figure in which all the surfaces or faces…

cone

a three-dimensional figure with one vertex and one circular b…

face

a flat surface of a polyhedron

Isometry

Congruence Transformation

Reflection

Line of Symmetry

Transformation that does not change the size, shape, or angle…

Transformation that does not change the size, shape, or angle…

Flip over a line.

The fold line where two halves match exactly.

Isometry

Transformation that does not change the size, shape, or angle…

Congruence Transformation

Transformation that does not change the size, shape, or angle…

union of a polygon and its interior

every polygonal region has a positive…

every polygonal region has a positive…

the area of a rectangle is the product…

polygonal region

congruent triangles have equal areas

the area of the polygonal region is equal to the sum of the a…

base and altitude

union of a polygon and its interior

polygonal region

every polygonal region has a positive…

congruent triangles have equal areas

Chord

Diameter

Arc

Central Angle

a segment whose endpoints are on the circle

a chord that contains the center of the circle

two points on a circle and all of the points on the circle ne…

an angle whose vertex is the center of the circle

Chord

a segment whose endpoints are on the circle

Diameter

a chord that contains the center of the circle

Area of a triangle

Law of sines

Law of Cosines

Inverse Signs

Area= 1/2 b•c sin A

Sin A Sin B Sin C... ----- = ---- = ----- ... a b c... Or variables o…

a2= b2+ c2 - 2bc cos A

inverse tan A = y, then sin-1(x)=m<A

Area of a triangle

Area= 1/2 b•c sin A

Law of sines

Sin A Sin B Sin C... ----- = ---- = ----- ... a b c... Or variables o…

Center

Chord

Secant

Point of Tangency

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

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 di…

Chord

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

transformation

preimage

image

rigid motion

function or mapping that results in a change in the position,…

the original figure

the resulting figure

a transformation that preserves distance and angle measures

transformation

function or mapping that results in a change in the position,…

preimage

the original figure