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Similar Triangles

Congruent Triangles

Equilateral Triangles

Proportional

Triangles with equal angles. ... Triangles that have the same s…

Triangles that are equal in every way. The three sides and th…

A triangle in which all three sides are equal.

When two quantities always have the same size in relation to…

Similar Triangles

Triangles with equal angles. ... Triangles that have the same s…

Congruent Triangles

Triangles that are equal in every way. The three sides and th…

radius

chord

diameter

tangent

any line segment that connects the center with a point on the…

a line segment that connects two points on the circle

a chord that passes through the center of the circle... the lon…

a line the intersects a circle in exaclty one point

radius

any line segment that connects the center with a point on the…

chord

a line segment that connects two points on the circle

Circle (definition)

Radius (definition)

Diameter (definition)

Radius (picture)

All points are the same distance from the center

The distance from the center to the edge of a circle

Starts at one side of the circle, goes through the center and…

Circle (definition)

All points are the same distance from the center

Radius (definition)

The distance from the center to the edge of a circle

Circumference

Cyclic quadrilateral

Externally tangent (circles)

Inscribed (in a circle, semicircle, or…

The distance around a circle, given by the formula C=2πr, whe…

A quadrilateral that can be inscribed in a circle

Intersecting at exactly the one point, with neither circle in…

Having each vertex on the circle, semicircle, or sphere. Usua…

Circumference

The distance around a circle, given by the formula C=2πr, whe…

Cyclic quadrilateral

A quadrilateral that can be inscribed in a circle

Chord

Diameter

Tangent

Point of tangency

Line SEGMENT whose endpoints lie on circle

A chord that passes through the center of a circle (longest c…

A line that intersects the circle at only one point

the point where the tangent intersects with circle

Chord

Line SEGMENT whose endpoints lie on circle

Diameter

A chord that passes through the center of a circle (longest c…

Circle

Center

Radius

Diameter

the set of all points in a plane that are equidistant from a…

the given point that all points are equidistant from

distance from the center to a point on the circle; segment wh…

distance across the circle, through the center (twice the rad…

Circle

the set of all points in a plane that are equidistant from a…

Center

the given point that all points are equidistant from

radius

Diameter

center

chord

A line segment with one endpoint at the center of a circle an…

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

Center = is equal distance from all edges of a circle

a straight line connecting two points on a circle... can neve…

radius

A line segment with one endpoint at the center of a circle an…

Diameter

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

congruent circles

concentric circles

radius

chord

Circles with congruent radii

Circles that lie in the same plane and have the same center

A straight line from the center to the circumference of a cir…

a straight line connecting two points on a circle... can neve…

congruent circles

Circles with congruent radii

concentric circles

Circles that lie in the same plane and have the same center

Circle

Congruent Circles

Concentric Circles

Minor Arcs

A set of points equidistant from a point (the center)

Circles the same shape and same size (radius)

Circles that have the same center

Arc measure less than 180

Circle

A set of points equidistant from a point (the center)

Congruent Circles

Circles the same shape and same size (radius)

Circle

Center

Radius

Diameter

Set of all points in a plane that are equidistant from a give…

Given point in a circle that all points are equidistant from

Segment who is an points are the center and any point on the…

Chord that contains the center of the circle

Circle

Set of all points in a plane that are equidistant from a give…

Center

Given point in a circle that all points are equidistant from

circle

circumference

radius

diameter

a set of lines which are equidistant to one another from the…

the perimeter (length around the outside) of a circle

a line from the centre point to any point on the circumference

a line joining two point on the circumference and passing thr…

circle

a set of lines which are equidistant to one another from the…

circumference

the perimeter (length around the outside) of a circle

Radius

Congruent Circles

Concentric Circles

Semicircle

Line segment that connects the center to a point on the circle

Circles what have the same radius

Circles that have the same center

An arc that measures 180 degrees

Radius

Line segment that connects the center to a point on the circle

Congruent Circles

Circles what have the same radius

center of the circle

circle

circumference

radius (radii)

The point at the exact center of a circle. All points on a ci…

A geometric figure consisting of all the points on a plane th…

The distance around a circle.

A line segment that has one endpoint at the center of a circl…

center of the circle

The point at the exact center of a circle. All points on a ci…

circle

A geometric figure consisting of all the points on a plane th…

Chord

Tangent

Inscribed Angle

Central Angle

A line segment in the circle that intersects two sides of the…

A line that intersects the circle at one point.

An angle whose vertex is on the circle and is half the arc it…

An angle whose vertex is at the center of the circle and is e…

Chord

A line segment in the circle that intersects two sides of the…

Tangent

A line that intersects the circle at one point.

Circle

Center of a circle

Radius

Chord

A line forming a closed loop, every point on which is a fixed…

A point inside the circle. All points on the circle are equid…

the distance from the center of a circle to the edge

a line that connects one point on a circle to another point o…

Circle

A line forming a closed loop, every point on which is a fixed…

Center of a circle

A point inside the circle. All points on the circle are equid…

Chord

Secant

Tangent

Point of Tangency

segment whose endpoints are points on a circle

line that intersects a circle in two points

is a line in the plane of the circle that intersects the circ…

the point where a tangent line and circle intersect

Chord

segment whose endpoints are points on a circle

Secant

line that intersects a circle in two points

Chord

Secant

Tangent

Point of tangency

A segment whose endpoints lie on a circle.

A line that intersects a circle at 2 points

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

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 2 points

Congruent circles

Concentric Circles

Radius

Chord

two circles with the same radius

circles with the same center

the length of a line segment between the center and circumfer…

a straight line connecting two points on a curve

Congruent circles

two circles with the same radius

Concentric Circles

circles with the same center

Circle

Center

Radius

Chord

Set of all points in a plain that are equidistant from a give…

is equal distance from all edges of a circle

A straight line from the center to the circumference of a cir…

a segment whose endpoints are on a circle

Circle

Set of all points in a plain that are equidistant from a give…

Center

is equal distance from all edges of a circle

Def. circle

Radius

Chord

Diameter

The set of all points equidistant from a center

A segment from center to a point on a circle

A segment with both endpoints on the circle

A chord that intersects the center of the circle

Def. circle

The set of all points equidistant from a center

Radius

A segment from center to a point on a circle

Circle

Radius

Diameter

Chord

The set of all points that are equidistant from a given point

Distance from the center of a circle to a point on the circle

Distance across a circle through the center

Segment whose end points are points on the circle

Circle

The set of all points that are equidistant from a given point

Radius

Distance from the center of a circle to a point on the circle

Diameter

Radius

Circumference

Area

a line segment that passes through the center of a circle and…

a line segment with one endpoint at the center of a circle an…

the distance around a circle

the number of square units needed to cover a given surface

Diameter

a line segment that passes through the center of a circle and…

Radius

a line segment with one endpoint at the center of a circle an…

Circle

Radius

Chord

Diameter

Set of all points in a plane that are at a fixed distance fro…

A segment that joins the center of the circle to a point on t…

A line segment that joins two points of a circle

A chord that contains the center of the circle

Circle

Set of all points in a plane that are at a fixed distance fro…

Radius

A segment that joins the center of the circle to a point on t…

Interior/Exterior of a Circle

Chord

Secant

Concentric Circles

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

A chord is a segment whose endpoints lie on a circle

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

Concentric Circles are coplanar circles with the same center

Interior/Exterior of a Circle

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

Chord

A chord is a segment whose endpoints lie on a circle

Interior/Exterior of a Circle

Chord

Secant

Concentric Circles

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

A chord is a segment whose endpoints lie on a circle

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

Concentric Circles are coplanar circles with the same center

Interior/Exterior of a Circle

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

Chord

A chord is a segment whose endpoints lie on a circle

circle

center

radius

congruent circles

set of all points equidistant from a given point

point in the middle of a circle

a segment that has one endpoint at the center and the other e…

have congruent radii

circle

set of all points equidistant from a given point

center

point in the middle of a circle

Circle

Diameter

Radius

Circumference

The set of all points in a plane that are equidistant from a…

A segment that contains the center of a circle and has both e…

A segment that has one endpoint at the center and the other e…

The distance around the circle (C=2Pir)

Circle

The set of all points in a plane that are equidistant from a…

Diameter

A segment that contains the center of a circle and has both e…

Circle

Center of a Circle

Radius

Chord

The set of all points equidistant from a given point.

The point inside of a circle that is the same distance from e…

A segment with one endpoint on the center of the circle and t…

A segment with both end points on the circumference of the ci…

Circle

The set of all points equidistant from a given point.

Center of a Circle

The point inside of a circle that is the same distance from e…

Circle

Radius

Chord

Diameter

The set of all points that are equidistant from a point calle…

A segment whose endpoints are the center and any point on the…

A segment whose endpoints are on a circle.

A chord that contains the center of the circle.

Circle

The set of all points that are equidistant from a point calle…

Radius

A segment whose endpoints are the center and any point on the…

chord

diameter

radius

secant

A segment whose endpoints lie on a circle

A chord that passes through the center of the circle

A straight line from the center to the circumference of a cir…

A line that intersects a circle in two points

chord

A segment whose endpoints lie on a circle

diameter

A chord that passes through the center of the circle

Equation of a Circle

Equation of a Circle

- Center of a circle

Radius

(x-h)²+(y-k)²=r², (h, k) is the center, r is the radius.

(x-h)²+(y-k)²=r². ... *h and k are opposite signs, when identify…

(h , k)

The distance from the center of a circle to any point on the…

Equation of a Circle

(x-h)²+(y-k)²=r², (h, k) is the center, r is the radius.

Equation of a Circle

(x-h)²+(y-k)²=r². ... *h and k are opposite signs, when identify…

Circle

Pi (π)

Radius

Radii

A shape consisting of those points in a plane which are equid…

The ratio of the circumference to the diameter of a circle.

A line from the center of the circle of the circle to any poi…

more than 1 radius.

Circle

A shape consisting of those points in a plane which are equid…

Pi (π)

The ratio of the circumference to the diameter of a circle.

circle

radius

diameter

chord

a set of all points that are equidistant from the center of t…

a segment who's endpoints are the center of the circle and an…

a chord that passes through the center of the circle

a segment who's endpoints are on the circle

circle

a set of all points that are equidistant from the center of t…

radius

a segment who's endpoints are the center of the circle and an…

chord

circumference

diameter

radius

a line segment passing through a circle that has its endpoint…

the distance around a circle

a chord passing through the center of a circle

a line segment with one endpoint at the center of a circle an…

chord

a line segment passing through a circle that has its endpoint…

circumference

the distance around a circle

Circle

Radius

Chord

Diameter

The set of all points in a plane that are the same distance f…

The distance from the center of a circle to any point on the…

a straight line connecting two points on a circle... can neve…

A chord that passes through the center of the circle

Circle

The set of all points in a plane that are the same distance f…

Radius

The distance from the center of a circle to any point on the…

arc

endpoints

minor arc

major arc

a curved line along the circumference of a circle

the points where an arc ends

an arc that takes up less than half a circle

an arc that takes up more than half of a circle, ( must be la…

arc

a curved line along the circumference of a circle

endpoints

the points where an arc ends

Central Angle

Inscribed Angle

Cyclic Quadrilateral

Tangent Chord Angle

Central Angle = Intercepted Arc

Inscribed Angle = 1/2 Intercepted Arc

Opposite angles in a cyclic quadrilateral are supplementary.

Tangent Chord Angle = 1/2 Intercepted Arc

Central Angle

Central Angle = Intercepted Arc

Inscribed Angle

Inscribed Angle = 1/2 Intercepted Arc

Two Tangent Theorem

Chord-Chord Angle

Secant-Tangent Angle OR Tangent-Tangen…

Area of a sector

If 2 tangent segments are drawn to a circle from an external…

The measure of a chord-chord angle equals half the sum of the…

The measure of an angle whose vertex is OUTSIDE a circle is h…

Two Tangent Theorem

If 2 tangent segments are drawn to a circle from an external…

Chord-Chord Angle

The measure of a chord-chord angle equals half the sum of the…

Arc Length

Sector Area

Right-angle corollary

Arc-intercept corollary

measure of arc/360 x 2πr

measure of arc/360 x πr²

if an inscribed angle intercepts a semicircle, then the angle…

if two inscribed angles intercept the same arc, then they hav…

Arc Length

measure of arc/360 x 2πr

Sector Area

measure of arc/360 x πr²

Circle

Radius

Congruent circles

Concentric circles

A set of points equidistant from a given point

Segment from the center of a circle to the circle

Circles with the same (or equal) radius

Circles with the same center

Circle

A set of points equidistant from a given point

Radius

Segment from the center of a circle to the circle

Diameter

Radius

Chord

Segment

Is any chord drawn to the centre of the circle

Is any line drawn from the centre to the circumference

Is any straight line cutting the circumference of the circle…

Is an area cut off by a chord. There are major and minor segm…

Diameter

Is any chord drawn to the centre of the circle

Radius

Is any line drawn from the centre to the circumference

Tangent Conjecture

Tangent Segment Conjecture

Chord Central Angles Conjecture

Chord Arcs Conjecture

A tangent is perpendicular to the radius that intersects it.

Tangent segments from a point outside the circle are congruent.

Two congruent chords determine two congruent central angles.

Two congruent chords create two congruent arcs.

Tangent Conjecture

A tangent is perpendicular to the radius that intersects it.

Tangent Segment Conjecture

Tangent segments from a point outside the circle are congruent.

circumscribed angle

intercepted arc

center of a circle

adjacent arcs

An angle whose sides are tangent to a circle.

An arc that lies between two lines, rays, or segments.

The point from which all points on a circle are equidistant.

Arcs of a circle that have exactly one point in common.

circumscribed angle

An angle whose sides are tangent to a circle.

intercepted arc

An arc that lies between two lines, rays, or segments.

central angle

arc of a central angle

Total of all central angles

inscribed angle

An angle whose vertex is the center of the circle... Arc = Angle…

Equals the angle

equals 360 degrees

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

central angle

An angle whose vertex is the center of the circle... Arc = Angle…

arc of a central angle

Equals the angle