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Lines and Circles

Secant

Tangent

Central Angle

Secant - a line that intersects a circle in two points... Tangen…

If two lines intersect in the interior of a circle, then the…

A line is tangent to a circle if and only if the line is perp…

An angle whose vertex is the center of the circle

Lines and Circles

Secant - a line that intersects a circle in two points... Tangen…

Secant

If two lines intersect in the interior of a circle, then the…

Midpoint

Angle Bisector

Congruent

Magnitude

When you construct a perpendicular bisector of a segment, you…

A ray that divides an angle into two congruent angles is call…

If two angles, shapes or lines are equal in degree, length, a…

Translations can be accomplished by using a vector. Vectors a…

Midpoint

When you construct a perpendicular bisector of a segment, you…

Angle Bisector

A ray that divides an angle into two congruent angles is call…

Perpendicular Bisector Theorem

Angle Bisector Theorem

Triangle Midsegment Theorem

Triangle Inequality Theorem

If a pint is on the perpendicular bisector of a segment. then…

If a point is on the bisector of an angle, then it is equidis…

A Midsegment of a triangle is parallel to a side of a triangl…

The sum of any two side lengths of a triangle is greater than…

Perpendicular Bisector Theorem

If a pint is on the perpendicular bisector of a segment. then…

Angle Bisector Theorem

If a point is on the bisector of an angle, then it is equidis…

Point

Line

Plane

Collinear

A point names a location and has no size. It is represented b…

A line is a straight path that has no thickness and extends f…

A plane is a flat surface that has no thickness and extends f…

Points that lie on the same line.

Point

A point names a location and has no size. It is represented b…

Line

A line is a straight path that has no thickness and extends f…

Transversal

Corresponding Angles

Alternate Interior Angles

Same Side Interior Angles

a line that intersects 2 or more lines at different points

a pair of angles on the same side of a transversal (one inter…

a pair of angles on opposite sides of the transversal (non ad…

a pair of angles both interior on the same side of the transv…

Transversal

a line that intersects 2 or more lines at different points

Corresponding Angles

a pair of angles on the same side of a transversal (one inter…

vertex

adjacent angles

linear pair

vertical angles

the Endpoint where the rays join in an angle

Angles that have a common side and a common vertex (corner po…

A pair of adjacent angles whose non-common sides are opposite…

A pair of opposite congruent angles formed by intersecting li…

vertex

the Endpoint where the rays join in an angle

adjacent angles

Angles that have a common side and a common vertex (corner po…

interior

exterior

adjacent angles

vertical angles

area between the sides of an angle; the "inside"

area outside the sides of an angle

two coplanar angles with a common side, common vertex, and no…

two angles whose sides are opposite rays

interior

area between the sides of an angle; the "inside"

exterior

area outside the sides of an angle

Net Drawing

Isometric Drawing

Orthographic Drawing

Point

A 2-dimensional diagram that can be folded to form a 3-dimens…

A corner view of a 3-dimensional figure.

Shows 3 separate views of a 3-dimensional object: top view, f…

Indicates location and has no size. You can represent a point…

Net Drawing

A 2-dimensional diagram that can be folded to form a 3-dimens…

Isometric Drawing

A corner view of a 3-dimensional figure.

Right Triangle

Acute Triangle

Obtuse Triangle

Scalene Triangle

A triangle with exactly one right angle.

A triangle with all acute angles.

A triangle with exactly one obtuse angle.

A triangle with no congruent sides.

Right Triangle

A triangle with exactly one right angle.

Acute Triangle

A triangle with all acute angles.

Transversal

Corresponding Angles

Alternate Interior Angles

Alternate Exterior Angles

A line intersecting two or more other lines in the plane

Angles that occupy the same relative position at each interse…

Angles that are on opposite sides of a transversal, but not l…

Angles that are on opposite sides of a transversal, but not l…

Transversal

A line intersecting two or more other lines in the plane

Corresponding Angles

Angles that occupy the same relative position at each interse…

hypotenuse

similar figures

congruent figures

postulate

the largest side of a right triangle located across from the…

figures that have corresponding angles congruent and correspo…

figures that have corresponding angles congruent and correspo…

a statement that is accepted without proof

hypotenuse

the largest side of a right triangle located across from the…

similar figures

figures that have corresponding angles congruent and correspo…

perpendicular lines

concurrent lines

point of concurrency

circumcenter

Lines that meet at right angles

3 or more lines that meat in a common point

the point where concurrent lines meet

the point of concurrency of 3 perpendicular bisectors

perpendicular lines

Lines that meet at right angles

concurrent lines

3 or more lines that meat in a common point

Midsegment

Coordinate Proof

Perpendicular Bisector

Equidistant

A segment that connects the midpoints of two sides of a trian…

A proof involving placing geometric figures in a coordinate p…

A line that is perpendicular to a segment at its midpoint.

Equal distance

Midsegment

A segment that connects the midpoints of two sides of a trian…

Coordinate Proof

A proof involving placing geometric figures in a coordinate p…

segment bisector

sides of an angle

straight angle

supplementary angles

A point, ray, line, line segment, or plane that... intersects th…

The rays of an angle

An angle that has a measure of 180

Two angles whose measures have a sum of 180

segment bisector

A point, ray, line, line segment, or plane that... intersects th…

sides of an angle

The rays of an angle

Isosceles Triangle

Mid segment

Properties of midsegment

Equation for third side

A triangle that had at least two equal sides

Segment that connects two midpoints of two sides in a triangle

Parallel to third side, half the length of the third side,

2(midsegment)

Isosceles Triangle

A triangle that had at least two equal sides

Mid segment

Segment that connects two midpoints of two sides in a triangle

transversal

alternative interior angles

composite transformation

glide reflection

a line that intersects two or more lines

For two lines intersected by a transversal, a pair of nonadja…

More than one transformation is performed on a figure

combination of reflection and translation

transversal

a line that intersects two or more lines

alternative interior angles

For two lines intersected by a transversal, a pair of nonadja…

scalene

isosceles

equilateral

acute

a triangle with no sides congruent

a triangle with at least two sides congruent

a triangle with all sides congruent

a triangle with three acute angles

scalene

a triangle with no sides congruent

isosceles

a triangle with at least two sides congruent

parallel lines

skew lines

parallel planes

transversal

coplanar lines that do not intersect

non-coplanar lines that are neither parallel nor intersecting

planes that do not intersect

a line that intersects two or more coplanar lines in differen…

parallel lines

coplanar lines that do not intersect

skew lines

non-coplanar lines that are neither parallel nor intersecting

perpendicular bisector

point of concurrency

circumcenter

incenter

each point on this line is an equal distance from each endpoi…

The point at which three or more lines intersect.

the point of concurrency of the perpendicular bisectors of a…

the point of concurrency of the angle bisectors of a triangle

perpendicular bisector

each point on this line is an equal distance from each endpoi…

point of concurrency

The point at which three or more lines intersect.

Hinge Theorem

Converse of Hinge Theorem

Perpendicular Bisector

Locus

If two sides of a triangle are congruent to two sides of anot…

If two sides of a triangle are congruent to two sides of anot…

If a bisector is also perpendicular to a segment, it is a per…

Set of points that satisfies a particular condition

Hinge Theorem

If two sides of a triangle are congruent to two sides of anot…

Converse of Hinge Theorem

If two sides of a triangle are congruent to two sides of anot…

altitude of a triangle

centroid of a triangle

circumcenter of a triangle

circumscribed

a perpendicular segment from a vertex to the line containing…

the point of concurrency of the three medians of a triangle a…

the point of concurrency of the three perpendicular bisectors…

a circle that contains all of the vertices of a polygon.

altitude of a triangle

a perpendicular segment from a vertex to the line containing…

centroid of a triangle

the point of concurrency of the three medians of a triangle a…

hypotenuse

similar figures

congruent figures

posulate

the largest side of a right triangle located across from the…

figures that have corresponding angles congruent and correspo…

figures that have corresponding angles congruent and correspo…

a statement that is accepted without proof

hypotenuse

the largest side of a right triangle located across from the…

similar figures

figures that have corresponding angles congruent and correspo…

Hypotenuse

Similar figures

Congruent figures

Postulate

The largest side of a right triangle located across from the…

Figures that have corresponding angles congruent and congruen…

Figures that have corresponding angles congruent and correspo…

A statement that is accepted without a proof

Hypotenuse

The largest side of a right triangle located across from the…

Similar figures

Figures that have corresponding angles congruent and congruen…

congruent segments

non-collinear points

non-coplanar points

if-then statements

segments with equal measurement

points not on the same line

points not on the same plane

conditional statements (ex. if p, then q. P - hypothesis Q -…

congruent segments

segments with equal measurement

non-collinear points

points not on the same line

Linear Pair Postulate

Addition Property of Equality

Subtraction Property of Equality

Multiplication Property of Equality

If two angles form a linear pair, then they are supplementary

if you add the same number to both sides of an equation, the…

if you subtract the same number from both sides of an equatio…

if you multiply each side of an equation by the same number,…

Linear Pair Postulate

If two angles form a linear pair, then they are supplementary

Addition Property of Equality

if you add the same number to both sides of an equation, the…

circumcenter

perpendicular bisector

bisect

centroid

The point of currency of the perpendicular bisectors of the s…

Bisects a segment and is perpendicular to it.

to cut exactly in half

The point of concurrency of the medians of a triangle

circumcenter

The point of currency of the perpendicular bisectors of the s…

perpendicular bisector

Bisects a segment and is perpendicular to it.

perpendicular bisector

concurrent lines

circumcenter

incenter

A line that is perpendicular to a segment at its midpoint.

three or more lines that intersect at a common point

the point of concurrency of the perpendicular bisectors of a…

the point of concurrency of the angle bisectors of a triangle

perpendicular bisector

A line that is perpendicular to a segment at its midpoint.

concurrent lines

three or more lines that intersect at a common point

Midsegment

Midsegment Postulate

Perpendicular Bisector Postulate

Angle Bisector Postulate

A line segment that connects two midpoints of adjacent sides…

The midsegment of a triangle is parallel and half the length…

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

If a point is on the angle bisector of an angle, then it is e…

Midsegment

A line segment that connects two midpoints of adjacent sides…

Midsegment Postulate

The midsegment of a triangle is parallel and half the length…

Construct

Classifying Triangles

Acute Triangle

Right Triangle

A tangent from a point outside a given circle to the circle

All equilateral triangles are isosceles

Three angles, each less than 90 degrees

One angle equals 90 segrees

Construct

A tangent from a point outside a given circle to the circle

Classifying Triangles

All equilateral triangles are isosceles

Geometric Mean

Trigonometric Ratios

Inverse Trigonometric Ratios

Area of Triangle

Two positive numbers a and b is the positive number x that sa…

If sin A = x, then sin-1 x = measure of angle A

Geometric Mean

Two positive numbers a and b is the positive number x that sa…

Trigonometric Ratios

Skew Lines

Transversal

Corresponding Angles

Alternate Interior Angles

Lines that do not intersect and are not coplanar

A line that intersects at least two other lines

Matching positions when a transversal crosses at least two li…

Angles inside the lines and on opposite sides of the transver…

Skew Lines

Lines that do not intersect and are not coplanar

Transversal

A line that intersects at least two other lines

legs

slope angle

law of sines

inverse tangent

the two sides of a right triangle that form the right angle.…

the acute angle a line forms with the x-axis on a coordinate…

used to find measurements in non-right triangles using the si…

the "undo" of the tangent function

legs

the two sides of a right triangle that form the right angle.…

slope angle

the acute angle a line forms with the x-axis on a coordinate…

conditional statement

hypothesis

conclusion

if-then form

a logical statement with two parts, a hypothesis and a conclu…

the conditions that we are considering, the "if" part of the…

what follows as a result of the conditions in the hypothesis,…

a style of stating a conditional statement where the hypothes…

conditional statement

a logical statement with two parts, a hypothesis and a conclu…

hypothesis

the conditions that we are considering, the "if" part of the…

Point

Line

Plane

Line Segment

Has no dimension; It is a location on a plane.It is represent…

Has one dimension; It is an infinite set of points represente…

Has two dimensions extending without end; It is often represe…

Consists of two endpoints and all the points between them

Point

Has no dimension; It is a location on a plane.It is represent…

Line

Has one dimension; It is an infinite set of points represente…

undefined terms

line

plane

segment

cannot be defined by using other figures, most basic figures…

straight path that has no thickness and extends forever

flat surface that has no thickness and extends forever

part of a line consisting of two points and all points betwee…

undefined terms

cannot be defined by using other figures, most basic figures…

line

straight path that has no thickness and extends forever

plane

Opposite rays

plane

line

Is represented by a flat surface that extends without end and…

Two rays that share the same endpoint and form a line

Is represented by a flat surface that extends without end and…

Is represented by a straight path that extends in two opposit…

plane

Is represented by a flat surface that extends without end and…

Opposite rays

Two rays that share the same endpoint and form a line

Midsegment of a triangle

Perpendicular Bisector

Equidistant

Concurrent

A segment that connects the midpoints of two sides of a trian…

A line that is perpendicular to a segment at its midpoint.

A point that is the same distance from two objects.

When three or more lines, rays or segments intersect in the s…

Midsegment of a triangle

A segment that connects the midpoints of two sides of a trian…

Perpendicular Bisector

A line that is perpendicular to a segment at its midpoint.

line segment

between

congruent segments

construction

part of a line with two endpoints, labeled with 2 capital let…

in the middle, but not necessarily half way

Segments that have the same length (same size and shape)

to use tools to draw an object

line segment

part of a line with two endpoints, labeled with 2 capital let…

between

in the middle, but not necessarily half way

midsegment of a triangle

circumcenter of a triangle

concurrent

incenter of a triangle

a segment connecting the midpoints of two sides of a triangle

the point of concurrency of the perpendicular bisectors of a…

three or more lines that intersect at one point

the point of concurrency of the angle bisectors of a triangle

midsegment of a triangle

a segment connecting the midpoints of two sides of a triangle

circumcenter of a triangle

the point of concurrency of the perpendicular bisectors of a…

Perpendicular Bisector Theorem

Converse of Perpendicular Bisector The…

Angle Bisector Theorem

Converse of Angle Bisector Theorem

If a line is a perpendicular bisector, the two segments on ei…

If the two segments on either side of the bisector are congru…

If a point is on the bisector of an angle, the point is equid…

If a point in the interior of an angle is equidistant from th…

Perpendicular Bisector Theorem

If a line is a perpendicular bisector, the two segments on ei…

Converse of Perpendicular Bisector The…

If the two segments on either side of the bisector are congru…

Point

Line

Plane

Angle

A precise location or place on a plane

A basic term of geometry, it's made up of points and has no s…

a plane is a flat, two-dimensional surface that extends infin…

The space between two intersecting lines, measured in degrees.

Point

A precise location or place on a plane

Line

A basic term of geometry, it's made up of points and has no s…

Perpendicular Bisector

Perpendicular Bisector Theorem

Converse of the Perpendicular Bisector…

Concurrent Lines

A bisector that is perpendicular to the segment

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

If a point is equidistant from the endpoints of a segment the…

Three or more lines that intersect at a common point

Perpendicular Bisector

A bisector that is perpendicular to the segment

Perpendicular Bisector Theorem

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