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

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

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…

Absolute Value

Natural Number

Whole Number

Integer

the distance a number is from 0

counting numbers starting at 1, 2, 3, 4.....Not 0

counting numbers including 0.

the set of positive whole numbers, their opposites and 0

Absolute Value

the distance a number is from 0

Natural Number

counting numbers starting at 1, 2, 3, 4.....Not 0

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…

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…

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)

Net

Isometric Drawing

Orthographic Drawing

Point

Two-dimensional diagram that you can fold to form a thre-dime…

Shows a corner view of a three-dimensional figure

Another way to represent a 3-dimensional figure

A location; it has no size and no shape ... It is undefined

Net

Two-dimensional diagram that you can fold to form a thre-dime…

Isometric Drawing

Shows a corner view of a three-dimensional figure

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…

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…

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

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.

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.

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…

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…

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

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

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

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

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…

point

line

plane

collinear

a dot labeled by a capital letter

can be represented by anything straight and is labeled by any…

can be represented by any flat surface, is labeled by either…

points that all fall in one line

point

a dot labeled by a capital letter

line

can be represented by anything straight and is labeled by any…

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

find the measure of each interior angl…

the ratio of the side lengths of a qua…

find the geometric mean of the pair of…

some mountains in the alps are very st…

(n-2)180... =(45-2)180... =7740/4... =172

6x+2x+3x+7x=18=126... x=7... 2(7)=14

x^2=(2)(8)=16... x=4

tan^-1=(42.7/100)... =23

find the measure of each interior angl…

(n-2)180... =(45-2)180... =7740/4... =172

the ratio of the side lengths of a qua…

6x+2x+3x+7x=18=126... x=7... 2(7)=14

Remote Interior Angles of a Triangle

Triangle Sum Theorem

Exterior Angle Theorem

30-60-90 Triangle Theorem

2 sides of a triangle not adjacent to exterior angles

the sum of the measures of the interior angles of a triangle…

the measure of the exterior angle of a triangle is equal to t…

Remote Interior Angles of a Triangle

2 sides of a triangle not adjacent to exterior angles

Triangle Sum Theorem

the sum of the measures of the interior angles of a triangle…

Circle

Center

Radius

Chord

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

the point inside a circle that is the same distance from all…

a segment with one endpoint at the center of the circle and t…

a segment whose endpoints are any two points on the circle

Circle

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

Center

the point inside a circle that is the same distance from all…

Paralellogram

Rectangle

Rhombus

Square

1. Opp <s congruent ... 2. Opp sides congruent... 3. Diagonals bise…

1. All props of pgrams... 2. Diagonals are = ... 3. 4 right <s

1. All props of pgrams... 2. 4 = sides... 3. Diagonals bisect <s... 4.…

1. All props of pgrams, rectangles, and rhombi

Paralellogram

1. Opp <s congruent ... 2. Opp sides congruent... 3. Diagonals bise…

Rectangle

1. All props of pgrams... 2. Diagonals are = ... 3. 4 right <s

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

Altitude

Acute Triangle

Angle Bisector

Base angle

the height of an object or point in relation to sea level or…

An acute triangle is a triangle with all three angles acute (…

angle bisector theorem is concerned with the relative lengths…

base angles have the same degree measure and are, as a result…

Altitude

the height of an object or point in relation to sea level or…

Acute Triangle

An acute triangle is a triangle with all three angles acute (…

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…

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).

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.

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…

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 (…

Similar

Similarity Ratio

Similarity Transformation

Indirect Measurement

Have the same shape but not necessarily the same size.

Ratio of lengths of the corresponding sides of two similar po…

A dilation or a composite of one or more dilation a and one o…

Any method that uses formulas, similar figures, and/or propor…

Similar

Have the same shape but not necessarily the same size.

Similarity Ratio

Ratio of lengths of the corresponding sides of two similar po…

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…