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Three non-collinear

Two

Two intersecting

Four non-coplanar

_____ _______points determine exactly one plane.

____ points determine exactly one line.

_____ ______ planes form a line.

_____ ______ points determine space.

Three non-collinear

_____ _______points determine exactly one plane.

Two

____ points determine exactly one line.

Point

Line

Plane

Collinear Points

Indicates a location represented by a dot

Represented by a straight path that extends in 2 opposite dir…

Represented by a flat surface that extends without end and ha…

Points that all lie on the same line

Point

Indicates a location represented by a dot

Line

Represented by a straight path that extends in 2 opposite dir…

Geometry

Set

Finite Set

Infinite Set

branch of mathematics that defines and relates the basic prop…

a collection of distinct objects with common characteristics

a set whose elements can be counted

a set whose elements cannot be counted

Geometry

branch of mathematics that defines and relates the basic prop…

Set

a collection of distinct objects with common characteristics

Point

Midpoint

Line

Plane

It is a location that is undefined.

Point that divides a segment into two congruent.

A series of points that extend in two directions infinitely t…

A flat surface that has no thickness.

Point

It is a location that is undefined.

Midpoint

Point that divides a segment into two congruent.

point

line

line segment

segment addition postulate

location in space

determined by two points, extends forever in opposite directi…

determined by two points, part of a line, begins and ends at…

line segment lengths can be determined by comparing the sum o…

point

location in space

line

determined by two points, extends forever in opposite directi…

Point

Line

Plane

Line Segment

Undefined term in Euclidean Geometry. A location in space. No…

Undefined term in Euclidean Geometry. The straight path of a…

Undefined term in Euclidean Geometry. The straight path of a…

A portion of a line that has definite length, and two endpoin…

Point

Undefined term in Euclidean Geometry. A location in space. No…

Line

Undefined term in Euclidean Geometry. The straight path of a…

Parallel Lines

Skew Lines

Parallel Planes

If two parallel planes are cut by a th…

COPLANAR lines that do not intersect

NON coplanar lines that to not intersect (think left/right an…

Planes that do not intersect (Think floor and ceiling)

If planes X and Y are parallel, then their lines of intersect…

Parallel Lines

COPLANAR lines that do not intersect

Skew Lines

NON coplanar lines that to not intersect (think left/right an…

conjecture

counterexample

Collinear Points

Coplanar Points

an unproven statement based on observations.

an example that shows a conjecture is false.

Points that lie in the same line.

Points that lie in the same plane.

conjecture

an unproven statement based on observations.

counterexample

an example that shows a conjecture is false.

acute angle

adjacent angles

complementary angles

obtuse angle

an angle whose measure is less than 90 degrees

two angles that share a common side and vertex but do not sha…

two angles whose sum is 90 degrees

an angle whose measure is greater than 90 degrees (but less t…

acute angle

an angle whose measure is less than 90 degrees

adjacent angles

two angles that share a common side and vertex but do not sha…

Point

Line

Plane

Collinear

A point has no size.

Goes on forever in both directions.... Two points create a line.

A flat surface that has no thickness.... Three points create a p…

Points that lie on the same line.... Points E, F, & C are collin…

Point

A point has no size.

Line

Goes on forever in both directions.... Two points create a line.

What is a ray?

What is a segment?

What is a plane? How are they labeled?

What is a line?

A ray has an endpoint but extends forever in the other direct…

Has a starting and ending point and is a part of a line.

Has length and width but no thickness.... They intersect at a li…

Has length... No width or thickness... Extends forever in both dire…

What is a ray?

A ray has an endpoint but extends forever in the other direct…

What is a segment?

Has a starting and ending point and is a part of a line.

Perpendicular Lines

Linear Pair Theorem

Linear Pair Postulate

Angle Bisector

Lines that intersect to form right angles

If two angles form a linear pair then they are supplementary

If two angles form a linear pair then the sum of their measur…

A ray that divides an angle into two congruent angles

Perpendicular Lines

Lines that intersect to form right angles

Linear Pair Theorem

If two angles form a linear pair then they are supplementary

Kite

Trapezoid

Isosceles trapezoid

Rhombus

A 4-sided flat shape with straight sides that has two pairs o…

A trapezoid is a 4-sided flat shape with straight sides that…

the sides that aren't parallel are equal in length and both a…

a four-sided shape where all sides have equal length; opposit…

Kite

A 4-sided flat shape with straight sides that has two pairs o…

Trapezoid

A trapezoid is a 4-sided flat shape with straight sides that…

Point

Line

Plane

Collinear

Undefined. No size, thickness, represents location, all other…

Undefined term. No thickness, goes on forever in opposite dir…

Undefined term. No thickness. Flat surface that extends infin…

points all in one line

Point

Undefined. No size, thickness, represents location, all other…

Line

Undefined term. No thickness, goes on forever in opposite dir…

segment

ray

angle

sides of an angle

a part of a line bound by two distinct end points

a line with a starting point, but no end point

the space between two intersecting, usually measured in degre…

two rays intersecting at their endpoints

segment

a part of a line bound by two distinct end points

ray

a line with a starting point, but no end point

Point

Line

Plane

Collinear

A location with no size or shape.

Made up of points with no thickness or width; Extends indefin…

A flat surface made up of points that extends indefinitely in…

Points that lie on the same line.

Point

A location with no size or shape.

Line

Made up of points with no thickness or width; Extends indefin…

scalene

isosceles

47º

78º

Find the measures of the sides of ∆ABC and classify the trian…

Find the measures of the sides of KPL and classify the triang…

m∠1=?

m∠2=?

scalene

Find the measures of the sides of ∆ABC and classify the trian…

isosceles

Find the measures of the sides of KPL and classify the triang…

Polygon

Net

Point

Line

a two d figure with 3 or more sides where each side meters (e…

a two d diagram of a 3 d figure, show all surfaces in one view

something that has a location but not an extension, where two…

a continuous extent of length, without breadth or thickness

Polygon

a two d figure with 3 or more sides where each side meters (e…

Net

a two d diagram of a 3 d figure, show all surfaces in one view

Inductive reasoning

conjecture

counterexample

point

reasoning based on patterns you observe

conclusion you reach using inductive reasoning

example for which the conjecture is incorrect

location

Inductive reasoning

reasoning based on patterns you observe

conjecture

conclusion you reach using inductive reasoning

Polygon

side of a polygon

vertex of a polygon

convex polygon

a closed plane with three or more line segments

each line segment that forms a polygon

each endpoint of a side of a polygon

a polygon such that no line containing a side of the polygon…

Polygon

a closed plane with three or more line segments

side of a polygon

each line segment that forms a polygon

point

line

line segment

ray

a location or position in space

an infinite set of points with no endpoints

two endpoints with all the points in between

part of a line, consisting of one endpoint and all the points…

point

a location or position in space

line

an infinite set of points with no endpoints

Incenter

Orthocenter

Midpoint Formula

Centroid/Medians

The point of concurrency of the three angle bisectors

The perpendicular segment from vertex of a triangle to the op…

A segment from vertex to midpoint. (steps: midpoint, slope, e…

Incenter

The point of concurrency of the three angle bisectors

Orthocenter

The perpendicular segment from vertex of a triangle to the op…

Perpendicular Bisector

Angle Bisector

Midline

Altitude

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

A ray, line or line segment that bisects an angle (cuts the a…

Segment that connects the midpoints of two sides of a triangle.

The segment connecting a vertex of a triangle drawn perpendic…

Perpendicular Bisector

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

Angle Bisector

A ray, line or line segment that bisects an angle (cuts the a…

the point that is equidistant from the…

coplanar lines that have a point in co…

the point of concurrency of the angle…

the point of intersection of the media…

circumcenter

concurrent lines

incenter

centroid

the point that is equidistant from the…

circumcenter

coplanar lines that have a point in co…

concurrent lines

Point

Line

Plane

Collinear

dot, location, no thickness

Goes on forever in both directions, no width... NOTATION: Alway…

Flat, continues infinitely, no thickness; ... IMAGE: is of two p…

Points that are on the same line... IMAGE: Points F, B and A are…

Point

dot, location, no thickness

Line

Goes on forever in both directions, no width... NOTATION: Alway…

Point

Line

Line segment

Ray

1. has no dimension... 2. represented by a dot... 3. named using on…

1. extends forever in one dimension... 2. has an arrowhead on ea…

1. part of a line that has 2 endpoints... 2. named by its endpoi…

1. part of a line with only one endpoint (initial point) and…

Point

1. has no dimension... 2. represented by a dot... 3. named using on…

Line

1. extends forever in one dimension... 2. has an arrowhead on ea…

Midpoint

Colinear

Acute

Obtuse

A point that divides a segment into two congruent parts

Three or more points on the same line

An angle that is less than a right angle

An angle that is more than a right angle but less than a stra…

Midpoint

A point that divides a segment into two congruent parts

Colinear

Three or more points on the same line

Segment Addition Postulate

Protractor Postulate

An angle can be named in 4 ways

Angle Addition Postulate

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

To find the measure in degrees of an angle, compute the absol…

For example : <abc ... 1. <1( if it has a number label)... 2. <b... 3.…

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

Segment Addition Postulate

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

Protractor Postulate

To find the measure in degrees of an angle, compute the absol…

Acute angle

Right angle

Obtuse angle

Straight angle

an angle whose measure is between 0 and 90 degrees

an angle whose measure is 90 degrees

an angle whose measure is between 90 and 180 degrees

an angle whose measure is 180 degrees

Acute angle

an angle whose measure is between 0 and 90 degrees

Right angle

an angle whose measure is 90 degrees

vertical angles

supplementary angles

complementary angles

vertical angles theorem

two angles whose sides form opposite rays

angles that add to 180

angles that add to 90

If 2 angles are vertical angles, then they are congruent

vertical angles

two angles whose sides form opposite rays

supplementary angles

angles that add to 180

Point

Line

Plane

Segment

An exact position or location

An infinite set of points extending in opposite directions.

A flat, infinite surface defined by three different points.

A set of points that extend from one endpoint to another. It…

Point

An exact position or location

Line

An infinite set of points extending in opposite directions.

Perpendicularity

Complimentary Angles

Supplementary Angles

Adjacent Angles

Lines, rays and segments that intersect at right angles

Angles whos sum is 90 degrees

Angles who's sum is 180 degrees

Share a common side or ray

Perpendicularity

Lines, rays and segments that intersect at right angles

Complimentary Angles

Angles whos sum is 90 degrees

inductive reasoning

conjecture

conditional

counterexample

reasoning based on patterns you observe

a conclusion you reach using inductive reasoning

if p then q

example that proves that a conclusion is not true

inductive reasoning

reasoning based on patterns you observe

conjecture

a conclusion you reach using inductive reasoning

Point

Line

Plane

collinear

Location; two lines intersect to form

made of points; no thickness or width; two planes intersect t…

flat surface; no thickness

points that are on the same line

Point

Location; two lines intersect to form

Line

made of points; no thickness or width; two planes intersect t…

parallelogram

rhombus

rectangle

square

quadrilateral with both pairs of opposite sides parallel

parallelogram with four congruent sides

parallelogram with four right angles

parallelogram with four congruent sides and four congruent an…

parallelogram

quadrilateral with both pairs of opposite sides parallel

rhombus

parallelogram with four congruent sides

line segment

ray

plane

line

Part of a line consisting of two points and all the points be…

The part of a line that starts at an end point and extends fo…

Flat surface that has no thickness and extends forever. Name:…

Straight path that has no thickness and extends forever. Name…

line segment

Part of a line consisting of two points and all the points be…

ray

The part of a line that starts at an end point and extends fo…

Line

collinear points

plane

coplanar

2 or more points joined with no thickness or width that exten…

points that lie on the same plane

flat 2 dimensional surface that extends indefinitely in all d…

objects that lie on the same plane

Line

2 or more points joined with no thickness or width that exten…

collinear points

points that lie on the same plane

Definition of Congruent Triangles

C.P.C.T.C

SSS Postulate

SAS Postulate

2 triangles are congruent if and only if their corresponding…

Corresponding parts of congruent triangles are congruent. ( D…

If 3 sides of one triangle are congruent to 3 sides of anothe…

If 2 sides and the included angle of 1 triangle are congruent…

Definition of Congruent Triangles

2 triangles are congruent if and only if their corresponding…

C.P.C.T.C

Corresponding parts of congruent triangles are congruent. ( D…

point

line

plane

collinear

a location, with no size or dimension

a "stream" of points that has no width or depth

a flat surface that extends indefinitely in all directions

points that lie on the same line

point

a location, with no size or dimension

line

a "stream" of points that has no width or depth

Right Angle Congruence Theorem

Vertical Angles Theorem

Congruent Supplements Theorem

Congruent Complements Theorem

If 2 angles are right angles, then they are congruent

If 2 angles are vertical angles, then they are congruent

If 2 angles are supplementary to the same angle or congruent…

If 2 angles are complementary to the same angle or congruent…

Right Angle Congruence Theorem

If 2 angles are right angles, then they are congruent

Vertical Angles Theorem

If 2 angles are vertical angles, then they are congruent