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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…

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

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…

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…

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

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

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

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…

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

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…

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

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

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…

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

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…

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

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…

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…

Point

Line

Plane

Space

All geometric figures consist of this. These are always repre…

This extends in two directions without ever ending. Any two p…

This extends in all directions, meaning it has no edges. It c…

A set of all points you are working with

Point

All geometric figures consist of this. These are always repre…

Line

This extends in two directions without ever ending. Any two p…

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

point

line

collinear

noncollinear

names a location and has no size; named by a single capital l…

a straight path that has zero thickness and extends forever i…

points that can be connected on the same line. any 2 points a…

3 or more points that cannot be connected on the same line.

point

names a location and has no size; named by a single capital l…

line

a straight path that has zero thickness and extends forever i…

Triangle Sum Theorem

Exterior Angle Theorem

Isosceles Triangle Theorem

Converse of Isosceles Triangle Theorem

The sum of the angle measures of a triangle is 180 degrees.

The measure of an exterior angle of a triangle is equal to th…

If 2 sides of a triangle are congruent, then the angles oppos…

If 2 angles of a triangle are congruent, then the sides oppos…

Triangle Sum Theorem

The sum of the angle measures of a triangle is 180 degrees.

Exterior Angle Theorem

The measure of an exterior angle of a triangle is equal to th…

Congruent/Congruent segment

Congruent Angles

Right Angles

Parallel lines

Lines that are the same length

Angles that are the same size

An angle that is measured to be 90°

A pair of lines that will never intersect with each other

Congruent/Congruent segment

Lines that are the same length

Congruent Angles

Angles that are the same size

Segment Addition Postulate

Ruler Postulate

Reflexive Property

Symmetric Property

If a point B lies on a line segment , then . That is, the dis…

on a number line, every point can be paired with a number and…

A quantity is congruent (equal) to itself. a = a

If a = b, then b = a

Segment Addition Postulate

If a point B lies on a line segment , then . That is, the dis…

Ruler Postulate

on a number line, every point can be paired with a number and…

Midpoint

Perpendicular Parallel Theorem

Parallel Parallel Theorem

Corresponding Angles Converse

divides a segment into 2 congruent pieces

if 2 lines are perpendicular to the same line, then they must…

if 2 lines are parallel to the same line, then they are paral…

if 2 lines are cut by a transversal, so that a pair of corr.…

Midpoint

divides a segment into 2 congruent pieces

Perpendicular Parallel Theorem

if 2 lines are perpendicular to the same line, then they must…

Supplementary Angles

Linear Pair

Adjacent Angles

Vertical Angles

Two angles are supplementary iff they add up to 180 degrees

A pair of adjacent angles is a linear pair iff the angles are…

Angles are Adjacent iff they share a common ray (are next to…

Angles are vertical iff they are opposite each other when two…

Supplementary Angles

Two angles are supplementary iff they add up to 180 degrees

Linear Pair

A pair of adjacent angles is a linear pair iff the angles are…

Perpendicular

4 Right Angles

Complementary

Then it's perpendicular to the other

If two lines intersect to form a linear pair of congruent ang…

If two lines are perpendicular then they intersect to form __…

If two sides of two adjacent acute angles are perpendicular t…

If a transversal is perpendicular to one of two parallel ____…

Perpendicular

If two lines intersect to form a linear pair of congruent ang…

4 Right Angles

If two lines are perpendicular then they intersect to form __…

Point Plotting Theorom

Angle Construction Postulate

Angle Addition Postulate

Linear Pair

Allows us to draw a segment of any given length.

Allows for you to create an angle out of any given size/measu…

Angle Addition Postulate if an angle is bisected the two inte…

When two lines intersect and it adds up to 180 degrees.

Point Plotting Theorom

Allows us to draw a segment of any given length.

Angle Construction Postulate

Allows for you to create an angle out of any given size/measu…

Altitude

Angle Bisector Theorem

Perpendicular Bisector Theorem

Median

In a triangle, a segment from a vertex of the triangle to the…

If a point is on the bisector of an angle, then it is equidis…

If a point is on the perpendicular bisector of a segment, the…

In a triangle, a line segment with endpoints that are the ver…

Altitude

In a triangle, a segment from a vertex of the triangle to the…

Angle Bisector Theorem

If a point is on the bisector of an angle, then it is equidis…

Triangle Sum Theorem

Exterior Angle Theorem

Flow Proof

Corollary

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

The measure of an interior angle of a triangle is equal to th…

A flow proof uses statements in boxes, with reasons beneath t…

A statement that follows directly from a theorem.

Triangle Sum Theorem

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

Exterior Angle Theorem

The measure of an interior angle of a triangle is equal to th…

acute angle

adjacent angles

altitude

angle bisector

An angle with a measure between 0° and 90°.

Two angles that share a common vertex and side, but have no c…

A segment that originates at the vertex of a triangle and mak…

A segment that divides an angle of a triangle into two equal…

acute angle

An angle with a measure between 0° and 90°.

adjacent angles

Two angles that share a common vertex and side, but have no c…

Point of Concurrency

Circumcenter

Angle Bisector

Incenter

Where three lines, segments, or rays intersect in a triangle

point of concurrency of the three perpendicular bisectors of…

A ray that divides an angle into two congruent (adjacent) ang…

the point of concurrency of the three angle bisectors in a tr…

Point of Concurrency

Where three lines, segments, or rays intersect in a triangle

Circumcenter

point of concurrency of the three perpendicular bisectors of…

Betweenness of points theorem

Betweenness of rays theorem

Complements of the same angle

Supplements of the same angle

A-B-C, then AB+BC=AC

OA-OB-OC, then <AOB+<BOC=<AOC

are equal

are equal

Betweenness of points theorem

A-B-C, then AB+BC=AC

Betweenness of rays theorem

OA-OB-OC, then <AOB+<BOC=<AOC

Triangle

Right Triangle

Obtuse Triangle

Acute Triangle

Any closed figure made by three line segments intersecting at…

When a triangle has one right angle.

When a triangle has one obtuse angle.

When all three angles in the triangle are acute.

Triangle

Any closed figure made by three line segments intersecting at…

Right Triangle

When a triangle has one right angle.