#### Study sets matching "geometry pre ap honors"

#### Study sets matching "geometry pre ap honors"

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

congruent

postulate

theorem

acute angle

identical in form; coinciding exactly when superimposed.

consists of a set of theorems, each derived from definitions,…

is a statement that has been proved on the basis of previousl…

An angle that measures less than ninety degrees but more than…

congruent

identical in form; coinciding exactly when superimposed.

postulate

consists of a set of theorems, each derived from definitions,…

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°

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"…

Substitution property

Reflexive property

Symmetric property

Transitive property

If a=b, then a can be substituted for b in any equation or ex…

Is used to prove congruence of geometric figures. This proper…

Property of equality for "a" and "b": if a=b then b=a

If a=b and b=c, then a=c (3 terms)

Substitution property

If a=b, then a can be substituted for b in any equation or ex…

Reflexive property

Is used to prove congruence of geometric figures. This proper…

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…

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…

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…

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.

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)

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…

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

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.

altitude

orthocenter

Triangular inequality theorem

median

a segment that extends from a vertice and is perpendicular to…

formed by 3 intersecting alititudes

any two sides of a triangle must add up to be longer than the…

segment that connects a vertice of a triangle with the midpoi…

altitude

a segment that extends from a vertice and is perpendicular to…

orthocenter

formed by 3 intersecting alititudes

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…

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…

undefined terms

collinear points

coplanar points

acute angle

words in geometry that are not formally defined... -point, line…

points on the same line

points in the same plane

angle less than 90 degrees

undefined terms

words in geometry that are not formally defined... -point, line…

collinear points

points on the same line

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…

undefined terms

collinear points

coplanar points

acute angle

words in geometry that are not formally defined... -point, line…

points on the same line

points in the same plane

angle less than 90 degrees

undefined terms

words in geometry that are not formally defined... -point, line…

collinear points

points on the same line

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…

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

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

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…

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…

Inductive reasoning

Conditional statement

Truth value

Conjecture

The process of reasoning that a rule or statement is true bec…

A statement that can be written "if P, then Q", where P is th…

A conditional statement can have a truth value of true or false

A statement believed to be true... Ex: a plant with leaves is a…

Inductive reasoning

The process of reasoning that a rule or statement is true bec…

Conditional statement

A statement that can be written "if P, then Q", where P is th…

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

Perpendicular bisector

Circumcenter

altitude

A line, ray, segment or plane that is perpendicular to a segm…

The point of concurrency of three perpendicular bisectors of…

The perpendicular segment from a vertex to the opposite side…

Perpendicular bisector

A line, ray, segment or plane that is perpendicular to a segm…

Circumcenter

The point of concurrency of three perpendicular bisectors of…

Postulate

Theorem

Conjecture

Inductive Reasoning

a truth without formal proof.

a statement that has been proved with facts.

a mathematical statement which appears to be true, but has no…

A form of reasoning in which a conclusion is reached based on…

Postulate

a truth without formal proof.

Theorem

a statement that has been proved with facts.

angle bisector

linear pair

midpoint

segment bisector

a ray that divides the angle into 2 congruent angles.... (∠bisec…

adjacent angles whose non common sides form a line

a point that divides a segment into 2 congruent segments

a point, segment, line, or plane that divides a line segment…

angle bisector

a ray that divides the angle into 2 congruent angles.... (∠bisec…

linear pair

adjacent angles whose non common sides form a line

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.

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

rational numbers

irrational number

real number

fraction

the quotient of two integers where the denominator does not e…

a number that does not repeat with a pattern

any number on a number line

the comparison of two numbers by division

rational numbers

the quotient of two integers where the denominator does not e…

irrational number

a number that does not repeat with a pattern

A circle that containd all the vertice…

circumcircle

the center of a circumcircle called th…

Circumcenter Theorem

circumscribed

a circle which passes through all the vertices of a polygon (…

Circumcenter

The perpendicular bisectors of the sides of a triangle inters…

A circle that containd all the vertice…

circumscribed

circumcircle

a circle which passes through all the vertices of a polygon (…

Incenter

Circumcenter

Median

Centroid

The point at which the three angle bisectors of a triangle ar…

The point at which the three perpendicular bisectors of the s…

A line segment formed by connecting a vertex of the triangle…

The point at which the medians of a triangle are concurrent.

Incenter

The point at which the three angle bisectors of a triangle ar…

Circumcenter

The point at which the three perpendicular bisectors of the s…