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

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

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

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°

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,…

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…

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…

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 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…

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)

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…

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

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

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

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…

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

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

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…

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…

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…

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.

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.

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

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

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…

Reflexive property of equality and ref…

Symmetric property of equality and ref…

Transitive property of equality and tr…

Substitution property of equality and…

A quantity is congruent or equal to itself. a=a

If a=b then b=a

If a=b and b=c, then a=c

A quantity may be substituted for it is equal for any express…

Reflexive property of equality and ref…

A quantity is congruent or equal to itself. a=a

Symmetric property of equality and ref…

If a=b then b=a

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

point

line

plane

collinear

a location and has no size

a straight path that extends in two opposite directions forever

a flat surface that extends without end and contains infinent…

points that lie on the same line

point

a location and has no size

line

a straight path that extends in two opposite directions forever

Congruent Polygons

Coresponding Parts of Congruent Triang…

Legs Of An Isoscleles Triangle

Base Of An Isosceles Triangle

Have congruent corresponding parts their matching sides and a…

Use after the triangles are congruent statement

The congruent sides of an isosceles triangle are its ...

The third side is the ...

Congruent Polygons

Have congruent corresponding parts their matching sides and a…

Coresponding Parts of Congruent Triang…

Use after the triangles are congruent statement

Point

Line

Plane

Coplanar Points

an exact location in space

an object with no thickness that extends infinitely in both d…

a flat surface that continues infinitely in all directions

points that lie on the same plane

Point

an exact location in space

Line

an object with no thickness that extends infinitely in both d…

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