#### 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…

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

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

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…

Formulas of a square base prism for P,…

Formulas of a trapezoidal prism for P,…

Formulas of a cylinder for C, B, LA, S…

Formulas of a square base pyramid for…

P- Add sides ... B- length by width... LA- Perimeter of base (P) ti…

P- Add the sides ... B- 1/2 height of the trapezoid (base 1+ bas…

C- 2r π... B- π r²... LA- Circumfrence times height ... SA- Lateral Ar…

P- number of sides times the side length... B- Side length²... LA-…

Formulas of a square base prism for P,…

P- Add sides ... B- length by width... LA- Perimeter of base (P) ti…

Formulas of a trapezoidal prism for P,…

P- Add the sides ... B- 1/2 height of the trapezoid (base 1+ bas…

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…

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…

LA of a prism

TA of a prism

LA of pyramid

TA of pyramid

The sum of the areas of all the LATERAL faces

LA plus the areas of the two bases

Just add up all the areas of the lateral faces

LA plus the area of the ONE base

LA of a prism

The sum of the areas of all the LATERAL faces

TA of a prism

LA plus the areas of the two bases

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…

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…

Similar

Proportionality

Theorem 12-1

Geometric mean

same shapes, not necessarily same size

given a, b, c and p, q, r, of positive real #'s, if a/p = b/q…

Similarity is an equivalence relation

if a, b, c, are positive #'s and a/b= b/c, then b is the geom…

Similar

same shapes, not necessarily same size

Proportionality

given a, b, c and p, q, r, of positive real #'s, if a/p = b/q…

Theorem 7.1 Perimeters of Similar Poly…

Postulate 7.1 Angle-Angle (AA) Similar…

Theorem 7.2 Side-Side-Side (SSS) Simil…

Theorem 7.3 Side-Angle-Side (SAS) Simi…

If two polygons are similar, then their perimeters are propor…

If two angles of one triangle are congruent to two angles of…

IF the corresponding side lengths of two triangles are propor…

If the lengths of two sides of one triangle are proportional…

Theorem 7.1 Perimeters of Similar Poly…

If two polygons are similar, then their perimeters are propor…

Postulate 7.1 Angle-Angle (AA) Similar…

If two angles of one triangle are congruent to two angles of…

Angle-Angle (AA) Similarity Postulate

Side-Side-Side (SSS) Similarity Theorem

Side-Angle-Side (SAS) Similarity Theorem

Triangle Proportionality Theorem

If two angles of one triangle are congruent to two angles of…

If the three sides of one triangle are proportional to the th…

If two sides of one triangle are proportional to two sides of…

If a line parallel to a side of a triangle intersects the oth…

Angle-Angle (AA) Similarity Postulate

If two angles of one triangle are congruent to two angles of…

Side-Side-Side (SSS) Similarity Theorem

If the three sides of one triangle are proportional to the th…

Lateral Area of a Pyramid

Lateral Area of a Prism

Lateral Area of a Cone

Lateral Area of a Cylinder

1/2 entire base x slant height (number of faces)

b x h for all faces

pi x radius x length

2 x pi x radius x height

Lateral Area of a Pyramid

1/2 entire base x slant height (number of faces)

Lateral Area of a Prism

b x h for all faces

Interior of a Circle

Exterior of a Circle

Chord

Secant

Set of small points inside the circle.

Set of points outside the circle.

A segment who's points lie on the circle

A line that intersects a circle at 2 points.

Interior of a Circle

Set of small points inside the circle.

Exterior of a Circle

Set of points outside the circle.

____ sides of a parallelogram are cong…

opposite angles of a parallelogram are…

diagonals of a parallelogram

If three or more parallel lines cut of…

opposite

congruent

bisect each other

they cut off congruent segments on every transversal

____ sides of a parallelogram are cong…

opposite

opposite angles of a parallelogram are…

congruent

Pythagorean Theorem and its Converse

45-45-90 Right Triangle Theorem

30-60-90 Right Triangle Theorem

Theorem 8.3

-If a triangle is a right triangle, then the sum of the squar…

-Both legs are congruent and then length of the hypotenuse is…

-Sum of the length of the hypotenuse is 2 times the length of…

-If the sum of the squares of 2 sides are greater than the sq…

Pythagorean Theorem and its Converse

-If a triangle is a right triangle, then the sum of the squar…

45-45-90 Right Triangle Theorem

-Both legs are congruent and then length of the hypotenuse is…

Vertical Angles Theorem

Congruent Supplements Theorem

Congruent Complements Theorem

Right Angle Congruence Theorem

Vertical angles are conguent.

If two angles are supplements of the same angle or a congruen…

If two angles are complements of the same angle, then the two…

All right angles are congruent

Vertical Angles Theorem

Vertical angles are conguent.

Congruent Supplements Theorem

If two angles are supplements of the same angle or a congruen…

Interior of a circle

Exterior of a circle

Chord

Secant

The set of all points inside the circle.

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

The set of all points inside the circle.

Exterior of a circle

The set of all points outside the circle.

The Theorem Just Called Theorem

Size-Change Preservation Properties Th…

Size-Change Distance Theorem

Figure Size-Change Theorem

The transformation S(k) that maps (x, y) onto (kx, ky) with k…

Every size transformation preserves: ... 1. Angle measure... 2. Bet…

Under any size change with magnitude k ≠ 0, the distance betw…

If a figure is determined by certain points, then its size-ch…

The Theorem Just Called Theorem

The transformation S(k) that maps (x, y) onto (kx, ky) with k…

Size-Change Preservation Properties Th…

Every size transformation preserves: ... 1. Angle measure... 2. Bet…

The Distance Formula

General Equation of a Circle

Two non vertical lines are parallel if…

Two non vertical lines are perpendicul…

The distance d between points (x1, y1) and (x2, y2) is given…

An equation of the circle with center (a,b) and radius r is (…

Their slopes are equal

The product of their slopes is -1

The Distance Formula

The distance d between points (x1, y1) and (x2, y2) is given…

General Equation of a Circle

An equation of the circle with center (a,b) and radius r is (…

T12-1

T12-2

T12-3

T12-4

the lateral area of a right prism equals the perimeter of a b…

the volume of a right prism equals the area of a base times t…

the lateral area of a regular pyramid equals half the perimet…

the volume of a pyramid equals one third the area of the base…

T12-1

the lateral area of a right prism equals the perimeter of a b…

T12-2

the volume of a right prism equals the area of a base times t…

12-1-1

12-1-2 (conv)

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 from a p…

If two segments from the same exterior point are tangent to a…

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

12-1-1

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

12-1-2 (conv)

If a line is perpendicular to the radius of a circle from a p…

Tangent to a circle

If a line is tangent to a circle,

If a line in the plane of a circle is…

If two tangent segments to a circle sh…

Line that intersects a circle exactly one point

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

then the line is tangent to the circle

then the two segments are congruent

Tangent to a circle

Line that intersects a circle exactly one point

If a line is tangent to a circle,

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

Parallel Postulate

Perpendicular Postulate

Corresponding Angles Theorem

Alternate Interior Angles Theorem

If there is a line and a point not on the line, then there is…

If there is a line and a point not on the line, then there is…

If two parallel lines are cut by a transversal, then the pair…

If two parallel lines are cut by a transversal, then the pair…

Parallel Postulate

If there is a line and a point not on the line, then there is…

Perpendicular Postulate

If there is a line and a point not on the line, then there is…

midpoint

Triangle Midsegment Theorem

Perpendicular Bisector Theorem

Converse of the Perpendicular Bisector…

a segment connecting the midpoint of two sides of a triangle

If a segment joins the midpoints of two sides of a... triangle,…

If a point is on the perpendicular bisector of a... segment, the…

If a point is equidistant from the... endpoints of a segment, th…

midpoint

a segment connecting the midpoint of two sides of a triangle

Triangle Midsegment Theorem

If a segment joins the midpoints of two sides of a... triangle,…

Theorem 2-1 Vertical Angles Theorem

Theorem 2-2 Congruent Supplements Theo…

Theorem 2-3 Congruent Complements Theo…

Theorem 2-4 All right angles are congr…

Vertical angles are conguent.

If two angles are supplements of the same angle or a congruen…

If two angles are complements of the same angle, then the two…

Theorem 2-1 Vertical Angles Theorem

Vertical angles are conguent.

Theorem 2-2 Congruent Supplements Theo…

If two angles are supplements of the same angle or a congruen…