#### 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…

Congruent central angles =

Congruent chords=

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

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 tange…

If 2 segments are tengent to a circle…

The segments are congruent

Inside

Outside

Chord

Secant

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

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

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 ________ th…

Outside

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

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 perpendicu…

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

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

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

Circle Tangency Thm

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

Converse of the Circle Tangency Thm

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

If a line is tangent to a circle, then…

If two tangent segments to a circle sh…

Within a circle, congruent angles have…

Within a circle, congruent central ang…

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

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…

If two tangent segments to a circle sh…

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 area…

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

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

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 area…

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 ex…

A line that intersects a circle at two points

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

Chord

A segment whose endpoints lie on a cirlce

Tangent

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

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 vertice…

segments connecting cooresponding vertices of the bases of a…

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…

If two segments tangent to a circle fo…

In a circle, or congruent circles, if…

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…

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 cir…

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 cir…

Arc length

The distance along an arc measured in linear units.

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 b…

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 re…

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

Applying the chord-chord product theor…

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 re…

...

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

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

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

Using tangent-secant and tangent-chord…

If two secants or chords intersect in…

Finding angle measures inside a circle…

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

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

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

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

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…

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 cen…

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 interce…

The area of a sector is a...

Fraction of the circle containing the sector.

To find the area of a sector whose cen…

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…

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

Its endpoints lie on the sides of the angle.

Half

Inscribed angle

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

Intercepted arc

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

Central angle

Arc

Minor arc definition

Minor arc measure

An angle whose vertex is the center of a circle.

An unbroken part of a circle consisting of two points called…

An arc whose points are on or in the interior of a central an…

The measure of a minor arc is equal to the measure of its cen…

Central angle

An angle whose vertex is the center of a circle.

Arc

An unbroken part of a circle consisting of two points called…

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 poi…

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

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 poi…