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ruler postulate

Segment Addition Postulate (Seg. Add.…

Protractor Postulate

Angle Addition Postulate

1.)points must be put on a number line... 2.)the distance betwee…

if B is between A and C, then AB+BC=AC (page 12 in book)

used to find the measure of an angle... 1.) take the absolute va…

m<AOB + m<BOC = m< AOC

ruler postulate

1.)points must be put on a number line... 2.)the distance betwee…

Segment Addition Postulate (Seg. Add.…

if B is between A and C, then AB+BC=AC (page 12 in book)

Supplementary Angles

Complementary Angles

Linear Pair

Vertical Angles

Angles that add to 180 degrees.... m<1+m<2=180

Two angles whose sum is 90 degrees.... m<1+m<2=90

A pair of adjacent angles whose noncommon sides are opposite…

A pair of opposite congruent angles formed by intersecting li…

Supplementary Angles

Angles that add to 180 degrees.... m<1+m<2=180

Complementary Angles

Two angles whose sum is 90 degrees.... m<1+m<2=90

Supplementary Angles

Complementary Angles

Linear Pair

Vertical Angles

Angles that add to 180 degrees.... m<1+m<2=180

Two angles whose sum is 90 degrees.... m<1+m<2=90

A pair of adjacent angles whose noncommon sides are opposite…

A pair of opposite congruent angles formed by intersecting li…

Supplementary Angles

Angles that add to 180 degrees.... m<1+m<2=180

Complementary Angles

Two angles whose sum is 90 degrees.... m<1+m<2=90

Collinear Points

Opposite Rays

Midpoint

Angle Bisector

Points that lie on the same line.

Are two rays that have a common end point. And form a line.

A point that divides a segment into two congruent segments.

A ray that divides an angle into two congruent angles.

Collinear Points

Points that lie on the same line.

Opposite Rays

Are two rays that have a common end point. And form a line.

Segment Addition Postulate

Angle Addition Postulate

Linear Pair Theorem

Vertical Angles Theorem

If b is between a and c, then ab + bc = ac.

If s is in the interior of angle PQR, then the measure of ang…

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

Vertical angles are congruent.

Segment Addition Postulate

If b is between a and c, then ab + bc = ac.

Angle Addition Postulate

If s is in the interior of angle PQR, then the measure of ang…

Proofs

Given

Prove

Reflexive

A logical statement helping to prove an idea being backed by…

The information given to help you prove a statement (the "if"…

What you are asked to show using the given(s) the reason (the…

Everything is equal to itself... ex: a=a

Proofs

A logical statement helping to prove an idea being backed by…

Given

The information given to help you prove a statement (the "if"…

Conjecture

Inductive Reasoning

Counterexample

Conditional Statement

An unproven statement that is based on observations.

You find a pattern in specific cases and then write a conject…

A specific case for which the conjecture is false.

A logical statement that has two parts, a hypothesis and a co…

Conjecture

An unproven statement that is based on observations.

Inductive Reasoning

You find a pattern in specific cases and then write a conject…

ruler postulate

Segment Addition Postulate (Seg. Add.…

Protractor Postulate

Angle Addition Postulate

1.)points must be put on a number line... 2.)the distance betwee…

if B is between A and C, then AB+BC=AC (page 12 in book)

used to find the measure of an angle... 1.) take the absolute va…

m<AOB + m<BOC = m< AOC

ruler postulate

1.)points must be put on a number line... 2.)the distance betwee…

Segment Addition Postulate (Seg. Add.…

if B is between A and C, then AB+BC=AC (page 12 in book)

complementary angles

supplementary angles

axiom/postulate

concave

two or more angles that add up to 90°

two or more angles that add up to 180°

a statement that is regarded as being true

to cave inwards

complementary angles

two or more angles that add up to 90°

supplementary angles

two or more angles that add up to 180°

Angle Sum Theorem

Perpendicular Bisector

Midsegment

Medians

The sum of the measures of the angles of a triangle is 180 de…

A segment that is perpendicular to the side and cuts the side…

A segment whose endpoints are midpoints of two sides of a tri…

A segment whose endpoints are a vertex of the triangle and th…

Angle Sum Theorem

The sum of the measures of the angles of a triangle is 180 de…

Perpendicular Bisector

A segment that is perpendicular to the side and cuts the side…

Paralellogram

Rectangle

Square

Rhombus

A four-sided polygon with two pairs of parallel and equal sid…

A parallelogram with 4 right angles.

A rectangle with 4 equal sides.

A parallelogram with 4 equal sides.

Paralellogram

A four-sided polygon with two pairs of parallel and equal sid…

Rectangle

A parallelogram with 4 right angles.

Point

Plane

Euclidean

Spherical

-An exact position or location on a plane surface... -Labeled wi…

-A flat surface that goes in every direction infinitely... -betw…

-the study of geometry based on definitions, undefined terms…

-the geometry of the two-dimensional surface of a sphere... -cur…

Point

-An exact position or location on a plane surface... -Labeled wi…

Plane

-A flat surface that goes in every direction infinitely... -betw…

point

plane

plane

Midpoint Theorem

if two lines intersect, then they intersect in exactly one __…

through a line and a point not in the line there is exactly o…

if two lines intersect, then exactly one _____ contains them

if M is the midpoint of line AB, then AM = ½AB and MB= ½AB

point

if two lines intersect, then they intersect in exactly one __…

plane

through a line and a point not in the line there is exactly o…

Corresponding Angles

Same-Side Interior Angles

Alternate Interior Angles

Alternate Exterior Angles

lie on the same side of the transversal and on the same sides…

lie on the same side of the transversal and between the inter…

nonadjacent angles that lie on opposite sides of the transver…

lie on opposite sides the transversal and outside the interse…

Corresponding Angles

lie on the same side of the transversal and on the same sides…

Same-Side Interior Angles

lie on the same side of the transversal and between the inter…

Pythagorean Theorem

30-60-90 triangle

45-45-90

sin

a^2 + b^2 = c^2

H= short leg × 2... Long leg = short leg√3... short leg = H÷2 or lo…

H= leg√2

opposite÷hypotenuse

Pythagorean Theorem

a^2 + b^2 = c^2

30-60-90 triangle

H= short leg × 2... Long leg = short leg√3... short leg = H÷2 or lo…

Midsegment of a triangle

Triangle Midsegment theorem

Equidistant

Perpendicular Bisector theorem

A segment connecting the midpoints of two sides of the triang…

If a segment joins the midpoint of two sides of a triangle, t…

A point is equidistant from two objects if it is the same dis…

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

Midsegment of a triangle

A segment connecting the midpoints of two sides of the triang…

Triangle Midsegment theorem

If a segment joins the midpoint of two sides of a triangle, t…

Equidistant

Concurrent

The Point of Concurrency

Circumvented of the Triangle

Point is the same distance from two or more objects.

Three or more lines intersect at one point.

Point where the concurrent lines intersect.

The point of concurrency.

Equidistant

Point is the same distance from two or more objects.

Concurrent

Three or more lines intersect at one point.

undefined term

line

collinear

segment

figures that cannot be defined by using other figures

straight path that has no thickness and extends forever

points that lie on the same line

is a part of a line consisting of two points and all the poin…

undefined term

figures that cannot be defined by using other figures

line

straight path that has no thickness and extends forever

Converse

Addition property

Subtraction property

Multiplication property

Swap hypothesis and conclusion q -> p

if a = b then a + c = b + c

if a = b then a - c = b - c

if a = b then ac = bc

Converse

Swap hypothesis and conclusion q -> p

Addition property

if a = b then a + c = b + c

point

line

plane

collinear points

exact location in space

defined by two points and extends infinitely in both directions

a flat surface having no boundaries

points in the same plane that lie on the same line

point

exact location in space

line

defined by two points and extends infinitely in both directions

Conjecture

Inductive Reasoning

Counterexample

Conditional Statement

An unproven statement that is based on observations.

You find a pattern in specific cases and then write a conject…

A specific case for which the conjecture is false.

A logical statement that has two parts, a hypothesis and a co…

Conjecture

An unproven statement that is based on observations.

Inductive Reasoning

You find a pattern in specific cases and then write a conject…

Ruler Postulate

Segment Addition Postulate

Define Congruence

Define Midpoint

To measure a coordinate

If B is between A and C, then AB + BC = AC

Same size and same shape

Bisects a segment

Ruler Postulate

To measure a coordinate

Segment Addition Postulate

If B is between A and C, then AB + BC = AC

Supplementary Angles

Complementary Angles

Linear Pair

Vertical Angles

Angles that add to 180 degrees.... m<1+m<2=180

Two angles whose sum is 90 degrees.... m<1+m<2=90

A pair of adjacent angles whose noncommon sides are opposite…

A pair of opposite congruent angles formed by intersecting li…

Supplementary Angles

Angles that add to 180 degrees.... m<1+m<2=180

Complementary Angles

Two angles whose sum is 90 degrees.... m<1+m<2=90

Corresponding angle converse

Alternate Interior Converse

Consecutive interior angle converse

Alternate exterior angle converse

if two lines are cut by a transversal so that the correspondi…

If two lines are cut by a transversal so that the interior an…

If two lines are cut by a transversal so that the consecutive…

If two lines are cut by a transversal so that the alternate e…

Corresponding angle converse

if two lines are cut by a transversal so that the correspondi…

Alternate Interior Converse

If two lines are cut by a transversal so that the interior an…

angle bisectors

perpendicular bisectors

altitude

medians

incenter (equidistant from sides)

circumcenter (equidistant from vertices)

orthocenter (perpendicular to sides but don't bisect)

centroid (length of segment of a median from the vertex to ce…

angle bisectors

incenter (equidistant from sides)

perpendicular bisectors

circumcenter (equidistant from vertices)

Point

Line

Collinear Points

Plane

Described simply as a location.

Described as a straight, continuous arrangement of an infinit…

Points that are located on the same line.

Described as a flat surface.

Point

Described simply as a location.

Line

Described as a straight, continuous arrangement of an infinit…

Ruler Postulate

Segment Addition Postulate

Protractor Postulate

Angle Addition Postulate

1. The points on a line can be paired with the real numbers i…

If B is between A and C, then AB + BC = AC

On line AB in a given plane, choose any point O between A and…

If point B lies in the interior of <AOC, then m<AOB + m<BOC =…

Ruler Postulate

1. The points on a line can be paired with the real numbers i…

Segment Addition Postulate

If B is between A and C, then AB + BC = AC

Point

Line

Collinear Points

Plane

A location; a point has no size and is denoted by a capital l…

A series of points that extend in two opposite directions wit…

Points that lie on the same line

A flat surface that has no thickness; contains many lines and…

Point

A location; a point has no size and is denoted by a capital l…

Line

A series of points that extend in two opposite directions wit…

Altitude

perpendicular bisector

Perpendicular lines

proportional sides

a line segment through a vertex and perpendicular to (i.e. fo…

perpendicular bisector is a special kind of segment, ray, or…

The relationship between two lines which meet at a right angl…

If the measures of the corresponding sides of two triangles a…

Altitude

a line segment through a vertex and perpendicular to (i.e. fo…

perpendicular bisector

perpendicular bisector is a special kind of segment, ray, or…

Point

Line

Plane

Intersection

No size, represents one location

2 points, no thickness, extends forever in both directions

3 points, no thickness, extends in all directions

Where points intersect

Point

No size, represents one location

Line

2 points, no thickness, extends forever in both directions

Net

Isometric Drawing

Orthographic Drawing

Point

A two-dimensional diagram that you can fold to form a three d…

Shows a corner view of a three dimensional figure. It allows…

Shows three separate views; a top, front, and a right side vi…

A location that has no size or shape. It is undefined.

Net

A two-dimensional diagram that you can fold to form a three d…

Isometric Drawing

Shows a corner view of a three dimensional figure. It allows…

altitude

acute triangle

angle bisector

base angle

a segment from the vertex of a triangle to the opposite side…

a triangle with all three sides acute (less than 90 degrees).

line or ray that divides an angle into two congruent angles.

side of a triangle from which the height is constructed.

altitude

a segment from the vertex of a triangle to the opposite side…

acute triangle

a triangle with all three sides acute (less than 90 degrees).

acute angle

adjacent angles

angle

collinear

angle whose measure is less than 90°

angles who share a common side

Area created by two rays or segments with common initial poin…

points lying on the same line ,segment , or Ray

acute angle

angle whose measure is less than 90°

adjacent angles

angles who share a common side

altitude

centroid

circumcenter of a triangle

circumscribed about

a line segment through a vertex and perpendicular to a line c…

the center of mass of a geometric object of uniform density

the point where three perpendicular bisectors of a triangle m…

drawing a figure around another, touching it at points but no…

altitude

a line segment through a vertex and perpendicular to a line c…

centroid

the center of mass of a geometric object of uniform density

Equivalent ratios

Proportion

Reciprocal property

Interchange Mean Property

Ratios that have the same simplified ratios

2 equal ratios

If two ratios are equal, then their reciprocals are also equal

If you interchange the means of a proportion, then you form a…

Equivalent ratios

Ratios that have the same simplified ratios

Proportion

2 equal ratios

Angle bisector

Incenter

In center location

In center distance

A ray that bisects an angle into two equal pieces.

The point where all three angle bi sectors intersect.

Always inside triangle

Equidistance from sides of triangle

Angle bisector

A ray that bisects an angle into two equal pieces.

Incenter

The point where all three angle bi sectors intersect.

Angle Bisector

Linear Pair

Midpoint

Segment Bisector

Ray is an angle bisector ↔ Divides angle into 2 congruent ang…

2 angles are linear pair ↔ they are adjacent angles whose non…

A point is a midpoint ↔ it divides a segment into 2 congruent…

A set of points is segment bisector ↔ intersection with the s…

Angle Bisector

Ray is an angle bisector ↔ Divides angle into 2 congruent ang…

Linear Pair

2 angles are linear pair ↔ they are adjacent angles whose non…

point

line

plane

line segment

undefined term, specific location, no dimension, represented…

undefined term, a connected straight path, continues forever

undefined term, a flat surface, extends forever

defined term, portion of a line consisting of two points and…

point

undefined term, specific location, no dimension, represented…

line

undefined term, a connected straight path, continues forever

Radius

Chord

Diameter

Circle

Is a segment with endpoints at the center and on the circle

Is a segment with endpoints on the circle

A chord that passes through the center and is made up of coll…

The set off all points in a plane equi distant from a given p…

Radius

Is a segment with endpoints at the center and on the circle

Chord

Is a segment with endpoints on the circle