# Study sets matching "geometry chapter 12 theorems"

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Theorem 12.1

Theorem 12.2

Theorem 12.3

Theorem 12.4

If a line is tangent to a circle then the line is perpendicula…

If a line in the plane of a circle is perpendicular to a radiu…

it two tangent segments to a circle share a common endpoint ou…

Within a circle or in congruent circles, congruent central ang…

Theorem 12.1

If a line is tangent to a circle then the line is perpendicula…

Theorem 12.2

If a line in the plane of a circle is perpendicular to a radiu…

All radii of a circle

If a line through the center of a circl…

If a line through the center of a circl…

The perpendicular bisector of a chord o…

Are equal

It also bisects the chord.

It is also perpendicular to the chord.

Contains the center of the circle.

All radii of a circle

Are equal

If a line through the center of a circl…

It also bisects the chord.

If a line is tangent to a circle

If 2 segments are tengent to a circle f…

Congruent central angles =

Congruent chords=

It is perpendicular to the radius drawn to the point of tangen…

The segments are congruent

Congruent chords

Congruent arcs

If a line is tangent to a circle

It is perpendicular to the radius drawn to the point of tangen…

If 2 segments are tengent to a circle f…

The segments are congruent

Sum of the areas of the lateral faces

Sum of the areas of the lateral faces +…

Sum of the areas of the lateral faces +…

2πrh

LA of a prism and pyramid

TA of a prism

TA of a pyramid

LA of a cylinder

Sum of the areas of the lateral faces

LA of a prism and pyramid

Sum of the areas of the lateral faces +…

TA of a prism

The Arc Addition Postulate

Corollary to the definition of a circle

Theorem 56

Theorem 57

If C is on A⌒B, then mA⌒C + mC⌒B = m A⌒C⌒B.

All radii of a circle are equal

If a line through the center of a circle is perpendicular to a…

If a line through the center of a circle bisects a chord that…

The Arc Addition Postulate

If C is on A⌒B, then mA⌒C + mC⌒B = m A⌒C⌒B.

Corollary to the definition of a circle

All radii of a circle are equal

Volume & Area of Prism

Volume & Area of Pyramid (not on test)

Volume & Area of Cylinder

Volume & Area of Cone

LA = ph (perimeter * height)... V = Bh (area of base * height)

LA = ½pl (½ * perimeter * slant height)... V = 1/3 Bh (1/3 * area…

LA = 2πrh (2 * π * radius * height)... Total area = LA + 2πr²... V =…

LA = πrl (π * radius * slant height)... TA = LA + πr²... V = 1/3πr²h

Volume & Area of Prism

LA = ph (perimeter * height)... V = Bh (area of base * height)

Volume & Area of Pyramid (not on test)

LA = ½pl (½ * perimeter * slant height)... V = 1/3 Bh (1/3 * area…

Theorem

Theorem

Theorem

Theorem

If a radius is perpendicular to a chord, then it bisects the c…

If a radius of a circle bisects a chord that is not a diameter…

The perpendicular bisector of a chord passes through the cente…

If two chords of a circle are equidistant from the center, the…

Theorem

If a radius is perpendicular to a chord, then it bisects the c…

Theorem

If a radius of a circle bisects a chord that is not a diameter…

chord

inscribed angle

intercepted arc

locus

a segment whose endpoints lie on a circle

an angle is inscribed in a circle if the vertex of the angle i…

an arc of a circle having endpoints on the sides of an inscrib…

a set of points, all of which meet a stated condition

chord

a segment whose endpoints lie on a circle

inscribed angle

an angle is inscribed in a circle if the vertex of the angle i…

Eulers theorem

Surface area of a right prism

Surface area of a right cylinder

Surface area of a regular pyramid

The number of faces, verticies, and edges of a polyhedron are…

The surface area of a right prism is the sum of the base areas…

The surface area of a right cylinder is the sum of the base ar…

The surface area of a regular pyramid is the sum of the base a…

Eulers theorem

The number of faces, verticies, and edges of a polyhedron are…

Surface area of a right prism

The surface area of a right prism is the sum of the base areas…

If a line is tangent to a circle, then…

If a line in the plane of a cricle is p…

If two tangent segments to a circle sha…

chord

perpendicular to the radius

tangent to the circle

congruent

segment whose endpoints are on a circle

If a line is tangent to a circle, then…

perpendicular to the radius

If a line in the plane of a cricle is p…

tangent to the circle

chord

inscribed angle

intercepted arc

locus

a segment whose endpoints are on the circle

if the vertex of the angle is on the circle and the sides of t…

an arc of a circle having endpoints on the sides of an inscrib…

a set of points, all of which meet a stated condition

chord

a segment whose endpoints are on the circle

inscribed angle

if the vertex of the angle is on the circle and the sides of t…

A line is tangent to a circle if and on…

If two segments are tangent to a circle…

Arc addition postulate

In a circle or two congruent circles...

It is perpendicular to the radius drawn to the point of tangen…

The segments are congruent

Measure of Arc=Measure of central angle

Congruent central angles have congruent chords...... Congruent ch…

A line is tangent to a circle if and on…

It is perpendicular to the radius drawn to the point of tangen…

If two segments are tangent to a circle…

The segments are congruent

Arc

Arc length

Central Angle of a Circle

Chord

unbroken part of the circle consisting of 2 points on the circ…

The distance along an arc measured in linear units.

An angle whose vertex is the center of a circle.

A segment whose endpoints lie on a circle.

Arc

unbroken part of the circle consisting of 2 points on the circ…

Arc length

The distance along an arc measured in linear units.

Interior of a circle ... 12-1

Exterior of a circle ... 12-1

Chord ... 12-1

Secant... 12-1

the set of all points inside the circle

is the set of all points outside the circle

a segment whose endpoints lie on a circle

a line that intersects a circle at two points

Interior of a circle ... 12-1

the set of all points inside the circle

Exterior of a circle ... 12-1

is the set of all points outside the circle

the measure of an inscribed angle

two inscribed angles that intercept the…

an angle inscribed in a semicircle

the opposite angles of a quadrilateral…

half the measure of its intercepted arc

are congruent

is right (90*)

supplementary

the measure of an inscribed angle

half the measure of its intercepted arc

two inscribed angles that intercept the…

are congruent

Euler's Theorem

Cross section

Lateral Faces

Lateral Edges

F+V=E+2

the intersection of a solid and a plane

parallelograms formed by connecting the corresponding vertices…

segments connecting cooresponding vertices of the bases of a p…

Euler's Theorem

F+V=E+2

Cross section

the intersection of a solid and a plane

Thm. 12-1-1

Thm. 12-1-2

Thm. 12-1-3

Arc Addition Postulate

If a line is tangent to a circle, then it is perpendicular to…

If a line is perpendicular to the radius of a circle at a poin…

If segments are tangent to a circle from the same external poi…

The measure of an arc formed by 2 adjacent arcs is the sum of…

Thm. 12-1-1

If a line is tangent to a circle, then it is perpendicular to…

Thm. 12-1-2

If a line is perpendicular to the radius of a circle at a poin…

Chord

Tangent

Secant

Point of tangency

A segment whose endpoints lie on a cirlce

A line in the same plane as a circle that intersects it at exa…

A line that intersects a circle at two points

Line which touches a circle or ellipse at just one point, alwa…

Chord

A segment whose endpoints lie on a cirlce

Tangent

A line in the same plane as a circle that intersects it at exa…

if a line is tangent to a circle,

if a line in the plane of a circle is p…

if two tangent segments to circle are a…

within a circle or in congruent circles…

then the line is perpendicular to the radius at the point of t…

then the line is tangent to the circle

then the two segments are congruent

congruent arcs

if a line is tangent to a circle,

then the line is perpendicular to the radius at the point of t…

if a line in the plane of a circle is p…

then the line is tangent to the circle

Tangent radius theorem

Congruent Tangent Segments

In the same circle or congruent circles…

In the same circle or congruent circles…

If a line is tangent to a circle, then the line is perpendicul…

Tangent segments drawn to a circle from the same point are con…

congruent central angles have congruent arcs

congruent chords cut off congruent arcs

Tangent radius theorem

If a line is tangent to a circle, then the line is perpendicul…

Congruent Tangent Segments

Tangent segments drawn to a circle from the same point are con…

Lateral faces

Base edges

Altitude

Height

faces that are not bases

where a lateral edge intersects a base

a segment from one base to another that is perpendicular to bo…

the length of the altitude

Lateral faces

faces that are not bases

Base edges

where a lateral edge intersects a base

Solid

Ployhedron

Flat

Edge

3D figure composed of flat and curved surfaces

Solid with all flat surfaces that encloses single region of sp…

Flat surface

Line segment at which 2 faces intersect

Solid

3D figure composed of flat and curved surfaces

Ployhedron

Solid with all flat surfaces that encloses single region of sp…

Thm. 12-1-1

Thm. 12-1-2

Thm. 12-1-3

Arc Addition Postulate

If a line is tangent to a circle, then it is perpendicular to…

If a line is perpendicular to the radius of a circle at a poin…

If segments are tangent to a circle from the same external poi…

The measure of an arc formed by 2 adjacent arcs is the sum of…

Thm. 12-1-1

If a line is tangent to a circle, then it is perpendicular to…

Thm. 12-1-2

If a line is perpendicular to the radius of a circle at a poin…