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two lines that do not intersect are ei…

two lines are _____ _____ if they do n…

two lines are _____ _____ if they do n…

||

parallel; skew

parallel lines

skew lines

symbol for "is parallel to"

two lines that do not intersect are ei…

parallel; skew

two lines are _____ _____ if they do n…

parallel lines

Parallel Lines

Perpendicular Lines

Skew Lines

Parallel Planes

Two lines that lie in the same plane but do not intersect

Two lines that if they intersect they form a right angle

Two lines that do not lie in the same plane and they never in…

Two planes that do not intersect

Parallel Lines

Two lines that lie in the same plane but do not intersect

Perpendicular Lines

Two lines that if they intersect they form a right angle

When two lines lie in the same plane a…

Lines that do not intersect and are no…

Similarly, if two planes do not inters…

Interior Angles

Parallel

Skew lines

Parallel planes

Angles on the inside of parallel lines cut by a transversal

When two lines lie in the same plane a…

Parallel

Lines that do not intersect and are no…

Skew lines

Polygon

Equilateral Polygon

Equiangular Polygon

Regular Polygon

A closed plane figure where the edges are not curved and each…

A polygon with all congruent sides.

A polygon with all congruent angles.

A polygon that is both equilateral and equiangular.

Polygon

A closed plane figure where the edges are not curved and each…

Equilateral Polygon

A polygon with all congruent sides.

Parallel Lines

Parallel Planes

Skew Lines

Transversal

Coplanar, equidistant, non-intersecting lines

Equidistant, non-intersecting planes

Non-coplanar, non-intersecting lines

Line that intersects two or more lines in a plane at differen…

Parallel Lines

Coplanar, equidistant, non-intersecting lines

Parallel Planes

Equidistant, non-intersecting planes

theorem 3-1

postulate 10

theorem 3-2

theorem

if two parallel planes are cut by a third plane, then the lin…

if two lines are cut by a transversal, the corresponding angl…

if two parallel lines are cut by a transversal, then alternat…

if two parallel lines are cut by a transversal, then alternat…

theorem 3-1

if two parallel planes are cut by a third plane, then the lin…

postulate 10

if two lines are cut by a transversal, the corresponding angl…

Alternate Interior Angles

Alternate Exterior Angles

Corresponding Angles

Same Side Interior Angles

Nonadjacent interior that lie on opposite sides of a transver…

Nonadjacent exterior angles that lie on opposite sides of the…

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

Interior angles that lie on the same side of the transversal.…

Alternate Interior Angles

Nonadjacent interior that lie on opposite sides of a transver…

Alternate Exterior Angles

Nonadjacent exterior angles that lie on opposite sides of the…

Post. Corresponding Angles Postulate […

Thm. Alternate Interior Angles Theorem…

Thm. Alternate Exterior Angles Theorem…

Thm. Same-Side Interior Angles Theorem…

If two parallel lines are cut by a transversal, then the pair…

If two parallel lines are cut by a transversal, then the pair…

If two parallel lines are cut by a transversal, then the two…

If tow parallel lines are cut by a transversal then the two p…

Post. Corresponding Angles Postulate […

If two parallel lines are cut by a transversal, then the pair…

Thm. Alternate Interior Angles Theorem…

If two parallel lines are cut by a transversal, then the pair…

reflexive property

substitution property

addition property

subtraction property

a=a

if a=b, then a can be substituted for b in any expression

if a=b, then a+c=b+c

if a=b, then a-c=b-c

reflexive property

a=a

substitution property

if a=b, then a can be substituted for b in any expression

parallel lines

intersecting lines

skew lines

parallel planes

coplanar lines that do not intersect

coplanar lines that have exactly one point in common

2 lines that do not lie on the same plane and do not intersect

planes that do not intersect

parallel lines

coplanar lines that do not intersect

intersecting lines

coplanar lines that have exactly one point in common

Parallel Lines

Vertical Angles

Supplementary Angles

Alternate Interior Angles

Coplanar lines that do not intersect

Two angles whose sides form two pairs of opposite rays

Two angles are supplementary if the sum of their measures is…

Nonadjacent interior angles that lie on opposite sides of the…

Parallel Lines

Coplanar lines that do not intersect

Vertical Angles

Two angles whose sides form two pairs of opposite rays

alternate exterior angles

alternate interior angles

consecutive interior angles

corresponding angles

In the figure, transversal t intersects lines a and m. Angles…

In the figure, transversal t intersects lines a and m. Angles…

In the figure, transversal t intersects lines a and m. Angles…

In the figure, transversal t intersects lines a and m. Angles…

alternate exterior angles

In the figure, transversal t intersects lines a and m. Angles…

alternate interior angles

In the figure, transversal t intersects lines a and m. Angles…

Parallel Lines

Skew lines

Transversal

Parallel Postulate

When two or more lines lie in the same plane and never inters…

Lines that are in different planes and never intersect.

A line that intersects two or more lines in different points

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

Parallel Lines

When two or more lines lie in the same plane and never inters…

Skew lines

Lines that are in different planes and never intersect.

Parallel Lines

Skew Lines

Parallel Planes

Transversal

coplanar lines that do not intersect

noncoplanar lies that do not intersect

planes that do not intersect

a line that intersects two or more coplanar lines

Parallel Lines

coplanar lines that do not intersect

Skew Lines

noncoplanar lies 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

theorem 19

theorem 20

theorem 21

theorem unnumbered #1

all radii of a circle are congruent

if two sides of a triangle are congruent, the angles opposite…

if two angles of a triangle are congruent, the sides opposite…

if two sides of a triangle are not congruent, the the angles…

theorem 19

all radii of a circle are congruent

theorem 20

if two sides of a triangle are congruent, the angles opposite…

Postulate 3-1 Same-side Interior Angle…

Theorem 3-1 Alternate Interior Angles…

Theorem 3-2 Corresponding Angles Theor…

Theorem 3-3 Alternate Exterior Angles…

supplementary... m∠1 + m∠2 = 180

congruent

corresponding

exterior

Postulate 3-1 Same-side Interior Angle…

supplementary... m∠1 + m∠2 = 180

Theorem 3-1 Alternate Interior Angles…

congruent

Skew Lines

Transversal

Corresponding Angles

Alternate Interior Angles

Lines that do not intersect and aren't coplanar.

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

Angles that occupy corresponding positions.

Angles that lie between the two lines on opposite sides of th…

Skew Lines

Lines that do not intersect and aren't coplanar.

Transversal

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

Slope means

Graph the following points on coordina…

Name the quadrant each of points are in:

Write the slope formula

rise/ run or the ______________ of a line

A- ... B- ... C- ... D- ... E- ... F-

m =

Slope means

rise/ run or the ______________ of a line

Graph the following points on coordina…

Scalene Triangle

Isosceles Triangle

Equilateral Triangle

Definition of Obtuse Triangle

A triangle is scalene IFF none of the sides are congruent

a triangle is isosceles IFF at least two of the sides are con…

A triangle is equilateral IFF all sides are congruent

a triangle is obtuse IFF it has one obtuse angle

Scalene Triangle

A triangle is scalene IFF none of the sides are congruent

Isosceles Triangle

a triangle is isosceles IFF at least two of the sides are con…

Parallel lines

Skew line

Parallel planes

Alternate interior angles

Coplanar lines that do not intersect. the symbol // mean " is…

Noncoplanar, they are not parallel and do not intersect

Plane that do not intersect

nonadjacent interior angles that lie on opposite sides of the…

Parallel lines

Coplanar lines that do not intersect. the symbol // mean " is…

Skew line

Noncoplanar, they are not parallel and do not intersect

Alternate Interior Angles

Alternate Exterior Angles

Corresponding Angles

Same Side Interior Angles

Nonadjacent interior that lie on opposite sides of a transver…

Nonadjacent exterior angles that lie on opposite sides of the…

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

Interior angles that lie on the same side of the transversal.…

Alternate Interior Angles

Nonadjacent interior that lie on opposite sides of a transver…

Alternate Exterior Angles

Nonadjacent exterior angles that lie on opposite sides of the…

Alternate Interior Angles

Alternate Exterior Angles

Corresponding Angles

Consecutive 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…

Two angles that are formed by two lines cut by a transversal…

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

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…

Parallel Lines

Skew Lines

Parallel Planes

Transversal

Two or more lines in the same plane that do not intersect

Two or more lines that are in different planes and do not int…

Two or more planes that do not intersect

A line that intersects two other coplanar lines at two differ…

Parallel Lines

Two or more lines in the same plane that do not intersect

Skew Lines

Two or more lines that are in different planes and do not int…

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

transversal

lines in the same plane that never intersect

lines that do not intersect and are not coplanar

planes that do not intersect

a line that intersects two or more lines

parallel lines

lines in the same plane that never intersect

skew lines

lines that do not intersect and are not coplanar

The Reflexive Property

The Substitution Property

The Addition Property

The Subtraction Property

a = a.

If a = b, then a can be substituted for b in any expression.

If a = b, then a + c = b + c.

If a = b, then a - c = b - c.

The Reflexive Property

a = a.

The Substitution Property

If a = b, then a can be substituted for b in any expression.

parallel lines

perpendicular lines

skew lines

parallel planes

coplanar lines that do not intersect

two lines that intersect at 90 angles

lines that do not intersect and are not coplanar

planes that do not intersect

parallel lines

coplanar lines that do not intersect

perpendicular lines

two lines that intersect at 90 angles

coinciding lines

intersecting lines

parallel lines

perpendicular lines

-same line... -have same slope... -have same y-intercept

-lines that intersect and have different slopes and different…

-have same slope... -have different y-intercepts

-have opposite reciprocal slopes... (slopes opposite)

coinciding lines

-same line... -have same slope... -have same y-intercept

intersecting lines

-lines that intersect and have different slopes and different…

parallel lines

skew lines

parallel planes

transversal

2 lines that are coplanar and do not intersect

2 lines that do not intersect and are not coplanar

2 planes that do not intersect

A line that intersects 2 or more coplanar lines at different…

parallel lines

2 lines that are coplanar and do not intersect

skew lines

2 lines that do not intersect and are not coplanar

parallel lines

perpendicular lines

parallel planes

line perpendicular to a plane

lines in the same plane that never intersect

Lines that intersect to form right angles

planes that do not intersect

a line that intersects the plane in a point and is perpendicu…

parallel lines

lines in the same plane that never intersect

perpendicular lines

Lines that intersect to form right angles

Parallel Lines

Skew Lines

Parallel Planes

Alternate Interior Angles

Coplanar lines that do not intersect. The symbol "II" means "…

Noncoplanar lines that are 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. The symbol "II" means "…

Skew Lines

Noncoplanar lines that are not parallel and do not intersect.

If all pairs of corresponding parts of…

If two polygons are congruent

The shortcut for "If there exists a co…

The shortcut for "If there exists a co…

then the polygons are congruent.

then all pairs of their corresponding parts are congruent.

SSS

SAS

If all pairs of corresponding parts of…

then the polygons are congruent.

If two polygons are congruent

then all pairs of their corresponding parts are congruent.

If two angles are complementary to the…

Complementary Angles

Adjecent Angles

Linear Pairs

... then they are equal (congruent).

Two angles whose sum is 90 degrees.

These are angles that have a common vertex and a common side…

A pair of adjacent angles whose exterior sides form a straigh…

If two angles are complementary to the…

... then they are equal (congruent).

Complementary Angles

Two angles whose sum is 90 degrees.

Transversal

Alternate Interior Angles

Corresponding Angles

Same-Side Interior Angles

A line that intersects two coplanar lines at two distinct poi…

Angles that lie within (inside, in the interior) a pair of li…

Angles formed by a transversal cutting through 2 or more line…

Two interior angles on the same side of the transversal... If t…

Transversal

A line that intersects two coplanar lines at two distinct poi…

Alternate Interior Angles

Angles that lie within (inside, in the interior) a pair of li…

parallel lines

skew line

parallels planes

transversal

two lines that do not intersect and are coplanar

two lines that do not intersect and are not coplanar

two planes that do not intersect

a line that intersect two or more coplanar lines at different…

parallel lines

two lines that do not intersect and are coplanar

skew line

two lines that do not intersect and are not coplanar

complementary angles

supplementary angles

adjacent angles

linear pair

Complementary angles are angles with measure that add to 90 d…

Supplementary angles are angles with measure that add to 180…

Adjacent angles are angles that have the same vertex, share a…

A linear pair is two adjacent angles who exterior sides form…

complementary angles

Complementary angles are angles with measure that add to 90 d…

supplementary angles

Supplementary angles are angles with measure that add to 180…

parallel lines

skew liines

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 liines

lines that do not intersect and are not coplanar

Slope

slope-intercept form

parallel line

perpendicular

rate of change = slope = m = (formula)

y = mx + b... M= slope... b = y- intercept (location where graph cr…

two lines that are parallel will have the same slope

two lines that are perpendicular have negative reciprocal slo…

Slope

rate of change = slope = m = (formula)

slope-intercept form

y = mx + b... M= slope... b = y- intercept (location where graph cr…

Parallel Lines

Perpendicular Lines

Parallel Planes

Skew Lines

Two or more lines which lie in the same plane and never inter…

Lines which intersect to form a right angle

Two or more planes which never intersect

noncoplanar lines that never intersect

Parallel Lines

Two or more lines which lie in the same plane and never inter…

Perpendicular Lines

Lines which intersect to form a right angle

Transversal

Alternate Interior Angles

Consecutive Interior Angles

Corresponding Angles

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

are inside the parallel lines, and on opposite (alternate) si…

lie on the same side of the transversal and on the interior o…

are two nonadjacent angles that lie on the ... same side of the…

Transversal

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

Alternate Interior Angles

are inside the parallel lines, and on opposite (alternate) si…