#### Study sets matching "geometry pre ap 10"

#### Study sets matching "geometry pre ap 10"

Circle

Center of the Circle

Center of a Regular Polygon

Apothem

Set of all points in a plane that are a fixed distance from a…

Point in middle of circle.

Equidistant from the vertices.

Distance from the center to a side.

Circle

Set of all points in a plane that are a fixed distance from a…

Center of the Circle

Point in middle of circle.

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°

Geometric Mean

Pythagorean theorem

Special Right Triangles

Trigonometry

For two positive numbers a and b, the geometric mean is the p…

a

**2+b**2=c*245

**, 45**, 90*?/x,x, x(to the square root of 2)... 30**, 60**, 90*/…SOH, CAH, TOA

Geometric Mean

For two positive numbers a and b, the geometric mean is the p…

Pythagorean theorem

a

**2+b**2=c*2Segment 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…

Radius

Chord

Diameter

Circumference

A segment with endpoints that are at the center and on the ci…

A segment with endpoints on the circle.

A chord that passes through the circle's center and made up o…

Distance around the circle.

Radius

A segment with endpoints that are at the center and on the ci…

Chord

A segment with endpoints on the circle.

Circle

Interior

Exterior

Chord

The set of all points in a plane equidistant from a given poi…

The points inside the circle

The points outside the circle

A segment whose endpoints are on the circle

Circle

The set of all points in a plane equidistant from a given poi…

Interior

The points inside the circle

Central Angle

Minor Arc

Major Arc

Semicircle

An angle whose vertex is at the center.

Part of a circle that is less than 180 degrees.

Part of the circle that is more than 180 degrees, but less th…

180 degrees in a circle.

Central Angle

An angle whose vertex is at the center.

Minor Arc

Part of a circle that is less than 180 degrees.

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"…

Adjacent arcs

Arc

Arc length

Center

Arcs in a circle that have exactly one point in common

A part of a circle that is defined by two endpoints

The distance between the end points along an arc measured in…

A given point

Adjacent arcs

Arcs in a circle that have exactly one point in common

Arc

A part of a circle that is defined by two endpoints

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…

Concentric Circle

Chord

Radius

Diameter

Coplanar circles that have the same center.

Segment with endpoints on the circle.

Segment with endpoints in the center. r= d/2

Chord that passes through the center. d= 2r

Concentric Circle

Coplanar circles that have the same center.

Chord

Segment with endpoints on the circle.

In the same or congruent circles, two…

In a circle, if the diameter is perpen…

If one chord is a perpendicular bisect…

In a circle or in congruent circles, t…

Their correspnoding chords are congruent

It bisects the chord and it's arc

The first chord is a diameter

They are equidistant from the center

In the same or congruent circles, two…

Their correspnoding chords are congruent

In a circle, if the diameter is perpen…

It bisects the chord and it's arc

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.

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…

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…

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

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.

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…

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)

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

congruent angles

vertical angles

adjacent angles

circumference

angles that have the same measure

opposite angles formed by two intersecting lines

pair of angles that share a vertex and one side

distance around the circle

congruent angles

angles that have the same measure

vertical angles

opposite angles formed by two intersecting lines

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

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

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…

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…

Circle

Center

Radius

Chord

The set of all points that are equidistant from a given point.

The given point as referred to in the definition of Circle.

The distance from the center to a point on the edge of a circ…

A segment that intersects the circle in two places.

Circle

The set of all points that are equidistant from a given point.

Center

The given point as referred to in the definition of Circle.

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.

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

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

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…

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.

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 (…