#### Study sets matching "geometry chapter 12 theorems"

#### Study sets matching "geometry chapter 12 theorems"

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

Inside

Outside

Chord

Secant

The interior of a circle is the set of all points ________ the…

The exterior of a circle is the set of all points ________ the…

A ________ is a segment whose end points lie on a circle

A ________ is a line that intersects a circle at two points

Inside

The interior of a circle is the set of all points ________ the…

Outside

The exterior of a circle is the set of all points ________ the…

Circle Tangency Thm

Converse of the Circle Tangency Thm

Snow Cone Theorem

Central Angle Chord Arc Theorem

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

If a line is in a plane of a circle is perpendicular to a radi…

The two segments tangent to a circle from a point outside the…

Within a circle/in congruent circles:... 1) Congruent cent ang ha…

Circle Tangency Thm

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

Converse of the Circle Tangency Thm

If a line is in a plane of a circle is perpendicular to a radi…

If a line is tangent to a circle, then.…

If two tangent segments to a circle sha…

Within a circle, congruent angles have.…

Within a circle, congruent central angl…

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

Then the two segments are congruent.

Have congruent arcs. (HO)

Have congruent chords. (HO)

If a line is tangent to a circle, then.…

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

If two tangent segments to a circle sha…

Then the two segments are congruent.

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…

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

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…

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

If a line is tangent to a circle, then.…

If a line in a plane is perpendicular t…

If two segments tangent to a circle for…

In a circle, or congruent circles, if y…

the line is perpendicular to the radius drawn to the point of…

the line is tangent to the circle

then the segments are congruent

you have congruent chords

If a line is tangent to a circle, then.…

the line is perpendicular to the radius drawn to the point of…

If a line in a plane is perpendicular t…

the line is tangent to the circle

Total area of a prism =

Lateral area of a right prism =

Volume of a right prism =

Lateral area of a cylinder =

lateral area + 2 times the area of a base (T.A. = L.A. + 2B).

the perimeter of a base times the height of the prism (L.A. =…

the area of a base times the height of the prism (V = B*h).

the circumference of a base times the height of the cylinder (…

Total area of a prism =

lateral area + 2 times the area of a base (T.A. = L.A. + 2B).

Lateral area of a right prism =

the perimeter of a base times the height of the prism (L.A. =…

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

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.

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…

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

The following theorem describes the rel…

Chord-Chord Product Theorem:... If two cho…

Applying the chord-chord product theore…

Secant segment

...

Then the products of the segments of the chords are equal.

A segment of a secant with at least one endpoint on the circle.

The following theorem describes the rel…

...

Chord-Chord Product Theorem:... If two cho…

Then the products of the segments of the chords are equal.

If a tangent and a secant (or chord) in…

Using tangent-secant and tangent-chord…

If two secants or chords intersect in t…

Finding angle measures inside a circle…

Then the measure of the angle formed is half the measure of it…

The measure of each angle formed is half the sum of the measur…

If a tangent and a secant (or chord) in…

Then the measure of the angle formed is half the measure of it…

Using tangent-secant and tangent-chord…

Chord

Secant

Tangent

Point of tangency

A segment whose endpoints lie on a circle

A line that intersects a circle at two points

A line in the same plane as a circle but only intersects the c…

The point where the tangent and a circle intersect

Chord

A segment whose endpoints lie on a circle

Secant

A line that intersects a circle at two points

The area of a sector is a...

To find the area of a sector whose cent…

Sector of a circle

Sector of a circle picture:

Fraction of the circle containing the sector.

A region bounded by two radii of the circle and their intercep…

The area of a sector is a...

Fraction of the circle containing the sector.

To find the area of a sector whose cent…

Inscribed angle

Intercepted arc

A chord or arc /subtends/ an angle if...

The measure of an inscribed angle is __…

An angle whose vertex is on a circle and whose sides contain c…

Consists of endpoints that lie on the sides of an inscribed an…

Its endpoints lie on the sides of the angle.

Half

Inscribed angle

An angle whose vertex is on a circle and whose sides contain c…

Intercepted arc

Consists of endpoints that lie on the sides of an inscribed an…