How can we help?

You can also find more resources in our Help Center.

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…

Parallel Lines

Skew Lines

Parallel Planes

Transversal Line

Coplanar lines that do not intersect.

Lines that do not intersect and are not coplanar.

Planes that do not intersect.

A line that intersects two or more coplanar lines at two diff…

Parallel Lines

Coplanar lines that do not intersect.

Skew Lines

Lines that do not intersect and are not coplanar.

Parallel lines

Skew lines

Parallel planes

Parallel Postulate

Coplanar lines that do not intersect

Lines that do not intersect and are not coplanar

Two planes that do not intersect

If there is a line and a point not on the line, then there is…

Parallel lines

Coplanar lines that do not intersect

Skew lines

Lines that do not intersect and are not coplanar

parallel lines

skew lines

parallel planes

parallel postulate

two lines if they do not intersect and are coplanar

two lines if they do not intersect and are not coplanar

two planes if they do not intersect

if there is a line and a point not on a line, then there is e…

parallel lines

two lines if they do not intersect and are coplanar

skew lines

two lines if they do not intersect and are not coplanar

Same-side Interior Angle Postulate... If…

Alternate Interior Angles Theorem... If a…

Corresponding Angles Theorem... If a tran…

Alternate Exterior Angles Theorem... If a…

supplementary... m∠1 + m∠2 = 180

congruent

corresponding

exterior

Same-side Interior Angle Postulate... If…

supplementary... m∠1 + m∠2 = 180

Alternate Interior Angles Theorem... If a…

congruent

parallel lines

skew lines

parallel planes

transversal

coplanar lines that don't intersect

noncoplanar; they aren't parallel and don't intersect

planes that don't intersect

a line that intersects two or more coplanar lines at distinct…

parallel lines

coplanar lines that don't intersect

skew lines

noncoplanar; they aren't parallel and don't intersect

Parallel Planes

Parallel Lines

Skew Lines

Transversal

Planes that do not intersect

Coplanar lines that don't intersect

Noncoplanar lines that don't intersect

A line that intersects two other lines

Parallel Planes

Planes that do not intersect

Parallel Lines

Coplanar lines that don't intersect

Parallel lines

Skew lines

Parallel planes

Transversal

Two lines that do not intersect and are coplanar

Lines that do not intersect and are not coplanar

Two planes that do not intersect

A line that intersects two or more coplanar lines at differen…

Parallel lines

Two lines that do not intersect and are coplanar

Skew lines

Lines that do not intersect and are not coplanar

Parallel

Skew

Transversal

Corresponding

Lines that do not intersect

Lines that do not intersect and are not coplanar

A line that intersect a set of parallel lines

A pair of angles that are in the "same spot" and do not touch…

Parallel

Lines that do not intersect

Skew

Lines that do not intersect and are not coplanar

Parallel lines

Skew Lines

Parallel Planes

Consecutive Interior Angles

Coplanar lines that do not intersect

Lines that do not intersect and are not coplanar

Planes that do not intersect

interior angles that lie on the same side of a transversal

Parallel lines

Coplanar lines that do not intersect

Skew Lines

Lines that do not intersect and are not coplanar

Parallel Lines

Skew lines

Parallel Planes

Transversal

Are coplanar lines that do not intersect.

Are lines that do not intersect and are not coplanar.

Are planes that do not intersect.

A line that intersects two or more coplanar lines at two diff…

Parallel Lines

Are coplanar lines that do not intersect.

Skew lines

Are lines that do not intersect and are not coplanar.

Parallel lines

Skew lines

Parallel planes

Transversal

coplanar lines that do not intersect

lines that do no intersect and are not coplanar

planes that do no intersect

a line that intersects two or more coplanar lines at two diff…

Parallel lines

coplanar lines that do not intersect

Skew lines

lines that do no intersect and are not coplanar

CPCTC

angle bisector

perpendicular bisector

Median

Corresponding ... Parts of ... Congruent ... Triangle are... Congruent

a ray that divides an angle into 2 congruent angles- max 3

a ray or segment that bisects a segment into 2 congruent segm…

a segment drawn from a vertex of a triangle to the midpoint o…

CPCTC

Corresponding ... Parts of ... Congruent ... Triangle are... Congruent

angle bisector

a ray that divides an angle into 2 congruent angles- max 3

Undefined Terms

Carefully Defined

Postulates

Theorems

Such as point, line, plane

Most terms in a mathematical system are

Basic properties accepted without proofs

Other properties established by proofs

Undefined Terms

Such as point, line, plane

Carefully Defined

Most terms in a mathematical system are

Parallel lines

Parallel planes

Rule 1

Corresponding angles

Lines which are coplanar and do not intersect

Planes that do not intersect

A line and a plane are parallel if they do not intersect

Two angles in corresponding positions relative to the two lin…

Parallel lines

Lines which are coplanar and do not intersect

Parallel planes

Planes that do not intersect

parallel lines

skew lines

transversal

alternate interior angles

coplanar lines that do not intersect

non coplanar lines ,they are neither parallel nor intersecting

a line that intersects two or more coplanar lines in differen…

two nonadjacent interior angles on opposite sides of the tran…

parallel lines

coplanar lines that do not intersect

skew lines

non coplanar lines ,they are neither parallel nor intersecting

Theorem

Alt Int ∠'s ≅

Alt Ext∠'s ≅

Same Side Int ∠'s Supp

If plane A is parallel to plane B and l is and element of A a…

If you have parallel lines cut by a transversal, then alterna…

If you have parallel lines cut by a transversal, then alterna…

If you have parallel lines cut by a transversal, then same si…

Theorem

If plane A is parallel to plane B and l is and element of A a…

Alt Int ∠'s ≅

If you have parallel lines cut by a transversal, then alterna…

Alternate Exterior Angles

Alternate Interior Angles

Corresponding angles

Distance From a Point to a Line

For two lines intersected by a transversal, a pair of angles…

For two lines intersected by a transversal, a pair of nonadja…

For two lines intersected by a transversal, a pair of angles…

The length of the perpendicular segment from the point to the…

Alternate Exterior Angles

For two lines intersected by a transversal, a pair of angles…

Alternate Interior Angles

For two lines intersected by a transversal, a pair of nonadja…

parallel lines

skew lines

parallel planes

transversal

coplanar lines that do not intersect

lines that do not intersect and are not coplanar

planes that do not instersect

a line that intersects two or more coplanar lines at two diff…

parallel lines

coplanar lines that do not intersect

skew lines

lines that do not intersect and are not coplanar

Parallel lines

Skew lines

Parallel planes

Postulate 13/14: Parallel/perpendicula…

Coplanar lines that do jot intersect

Non-Coplanar lines that do not intersect

Planes that do not intersect

If there is a line and a point not on that line, then there i…

Parallel lines

Coplanar lines that do jot intersect

Skew lines

Non-Coplanar lines that do not intersect

Parallel Lines

Skew Lines

Parallel Planes

Transversal

Coplanar lines that do not intersect

Lines that do not intersect and are NOT coplanar

Planes that do not intersect

A line that intersects two or more coplanar lines at two diff…

Parallel Lines

Coplanar lines that do not intersect

Skew Lines

Lines that do not intersect and are NOT coplanar

Parallel Lines

Skew Lines

Parallel Planes

Alternate Interior Angles

Coplanar lines that do not intersect; associated with ||

Noncoplanar; not parallel and do not intersect

Planes that do not intersect

Nonadjacent interior angles that lie on opposite sides of the…

Parallel Lines

Coplanar lines that do not intersect; associated with ||

Skew Lines

Noncoplanar; not parallel and do not intersect

Skew

Transversal

Corresponding angles

Alternate interior angles

No points in common, not in the same plane

A line which intersects two or more coplanar lines at differe…

Make an F shape

Make a Z shape, on opposite sides of the transversal and inne…

Skew

No points in common, not in the same plane

Transversal

A line which intersects two or more coplanar lines at differe…

sketch

draw

construct

segment bisector

make freehand

use a protractor and ruler to be sure angles and sides are ex…

use compass and straight edge, do not erase

a line, ray, or segment that passes through the midpoint of t…

sketch

make freehand

draw

use a protractor and ruler to be sure angles and sides are ex…

parallel lines

skew lines

parallel planes

transversal

are coplanar lines that do not intersect

are lines that do not intersect and are not coplanar

are planes that do not intersect

is a line that intersects two or more coplanar lines at two d…

parallel lines

are coplanar lines that do not intersect

skew lines

are lines that do not intersect and are not coplanar

Parallel Lines

Skew Lines

Parallel Planes

Transversal

coplanar lines that never intersect

lines that are not coplanar, not parallel, and don't intersect

planes that do not intersect

a line that intersects 2 or moe coplanar lines at distinct po…

Parallel Lines

coplanar lines that never intersect

Skew Lines

lines that are not coplanar, not parallel, and don't intersect

parallel lines

perpendicular lines

skew lines

parallel planes

( ‖ ) are coplanar and do not intersect.

( ⊥ ) lines that intersect at 90º angles.

lines that are not coplanar. Skew lines are not parallel and…

planes that do not intersect

parallel lines

( ‖ ) are coplanar and do not intersect.

perpendicular lines

( ⊥ ) lines that intersect at 90º angles.

parallel lines

skew lines

parallel planes

a line parallel to a plane

two lines that are coplanar and never intersect

two lines that are non coplanar

two planes that never intersect

a line and a plane that never intersect

parallel lines

two lines that are coplanar and never intersect

skew lines

two lines that are non coplanar

parallel lines

skew lines

parallel planes

parallel postulate

two lines if they do not intersect and are coplanar

two lines if they do not intersect and are not coplanar

two planes if they do not intersect

if there is a line and a point not on a line, then there is e…

parallel lines

two lines if they do not intersect and are coplanar

skew lines

two lines if they do not intersect and are not coplanar

Corresponding Angles Theorems

Alternate Interior Angles Theorem

Same-Side Interior Angles Postulate

Alternate Exterior Angles Theorem

If a transversal interactions two parallel lines, then corres…

If a transversal intersects two parallel lines, then alternat…

If a transversal intersects two parallel lines, then same-sid…

If a transversal intersects two parallel lines, then alternat…

Corresponding Angles Theorems

If a transversal interactions two parallel lines, then corres…

Alternate Interior Angles Theorem

If a transversal intersects two parallel lines, then alternat…

Parallel Lines

Skew Lines

Parallel Planes

Postulate 13: ... Parallel Postulate

coplanar lines that do not intersect

Lines that do not intersect and are not coplanar

two planes that do not intersect

If there is a line and a point not on the line, there is exac…

Parallel Lines

coplanar lines that do not intersect

Skew Lines

Lines that do not intersect and are not coplanar

Parallel lines

Skew lines

Parallel planes

Transversal

Two Lines that do not intersect and are coplanar

Lines that don't intersect and are not coplanar

Two planes that do not intersect

A line that intersects two or more coplanar lines at differen…

Parallel lines

Two Lines that do not intersect and are coplanar

Skew lines

Lines that don't intersect and are not coplanar

Parallel lines

Skew lines

Parallel planes

//

2 lines that do not intersect, but are coplanar

2 lines that do not intersect, but are not coplanar

2 planes that do not intersect

Parallel symbol

Parallel lines

2 lines that do not intersect, but are coplanar

Skew lines

2 lines that do not intersect, but are not coplanar

orthocenter

circumcenter

incenter

centroid

the point at which the three altitudes of a triangle intersect.

It is also the center of the circle circumscribed around a tr…

the point at which the angle bisectors of a triangle intersec…

the point at which the medians of a triangle intersect. It is…

orthocenter

the point at which the three altitudes of a triangle intersect.

circumcenter

It is also the center of the circle circumscribed around a tr…

Parallel lines

Perpendicular lines

Skew lines

Parallel planes

Coplanar lines that do NOT intersect; written as ||

Lines that intersect at a 90 degree angle; written as ⊥

NOT coplanar, NOT parallel, do NOT intersect lines

Planes that do NOT intersect

Parallel lines

Coplanar lines that do NOT intersect; written as ||

Perpendicular lines

Lines that intersect at a 90 degree angle; written as ⊥

Parallel Lines

Skew Lines

Parallel Planes

Transversal

Don't intersect and are coplanar

Two lines that don't intersect intersect and aren't coplanar

Two planes that don't intersect

A line that intersects two or more coplanar lines at differen…

Parallel Lines

Don't intersect and are coplanar

Skew Lines

Two lines that don't intersect intersect and aren't coplanar

Alternate Interior Angles

Alternate Exterior Angles

Corresponding Angles

Same Side Interior Angles

Angles that lie within a pair of lines and on opposite side o…

Angles that lie outside a pair of lines and on opposite sides…

Angles that lie on the same side of the traversal and in the…

Two angles that lie between the two lines on the same side of…

Alternate Interior Angles

Angles that lie within a pair of lines and on opposite side o…

Alternate Exterior Angles

Angles that lie outside a pair of lines and on opposite sides…

slope

slope-intercept form

point-slope form

slopes of parallel lines

the ratio of the vertical change to the horizontal change bet…

y = mx + b

y - y1 = m (x - x1)

If two nonvertical lines are parallel, then their slopes are…

slope

the ratio of the vertical change to the horizontal change bet…

slope-intercept form

y = mx + b

parallel lines

skew lines

parallel planes

interior angles

coplanar lines that do not intersect

lines that do not intersect and are not coplanar

planes that do not intersect

four angles that lie in the region between two lines

parallel lines

coplanar lines that do not intersect

skew lines

lines that do not intersect and are not coplanar

Triangles

Congruent, top

Size, shape

"Implies"

In congruent ______ all pairs of corresponding parts are cong…

In general, two geometric figures are _____ if one of them co…

Congruent figures have the same _____ and _____

-> means ("If then....")

Triangles

In congruent ______ all pairs of corresponding parts are cong…

Congruent, top

In general, two geometric figures are _____ if one of them co…

parallel lines

skew lines

transversal

alternate interior angles

-don't intersect... -coplanar

-don't intersect... -noncoplanar

a line that intersects two or more coplanar lines

two non adjacent interior angles on opposite sides of the tra…

parallel lines

-don't intersect... -coplanar

skew lines

-don't intersect... -noncoplanar

parallel lines

intersecting lines

skew lines

parallel planes

coplanar lines that never inersect

coplanar lines that share one point

2 lines that do not lie in the same plane AND do not intersect

planes that do not intersect

parallel lines

coplanar lines that never inersect

intersecting lines

coplanar lines that share one point

Triangle

Scalene triangle

Isosceles triangle

Equilateral triangle

A polygon with three sides

A triangle with no congruent sides

A triangle with at least two congruent sides

A triangle with all of its sides congruent

Triangle

A polygon with three sides

Scalene triangle

A triangle with no congruent sides