# Study sets matching "geometry theorems postulates"

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Theorem 2-1

Transversal

Postulate 10

Theorem 2-2

If two parallel planes are cut by a third plane, then the line…

A line that intersects two or more coplanar lines in different…

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

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

Theorem 2-1

If two parallel planes are cut by a third plane, then the line…

Transversal

A line that intersects two or more coplanar lines in different…

Postulate

Postulate

Postulate

Postulate

A line contains at least two points; a plane contains at least…

Through any two points there is exactly one line

Through any three points there is at least one plane, and thro…

If two points are in a plane, then the line that contains the…

Postulate

A line contains at least two points; a plane contains at least…

Postulate

Through any two points there is exactly one line

undefined term

point

line

plane

a word without a formal definition

undefined, a location with no size or dimension

undefined, a series of infinite points that extends in two dir…

undefined, flat surface that has no thickness and extends in a…

undefined term

a word without a formal definition

point

undefined, a location with no size or dimension

corresponding angles postulate

alternate interior angles theorem

consecutive interior angles theorem

alternate exterior angles theorem

if 2 parallel lines are cut by a transversal, then each pair o…

if 2 parallel lines are cut by a transversal, then each pair o…

if 2 parallel lines are cut by a tranversal, then each pair of…

if 2 parallel lines are cut by a transversal, then each pair o…

corresponding angles postulate

if 2 parallel lines are cut by a transversal, then each pair o…

alternate interior angles theorem

if 2 parallel lines are cut by a transversal, then each pair o…

Addition POE

Multiplication POE

Subtraction POE

Division POE

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

If a=b, then a times c = b times c

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

If a=b and c does not = 0, then a/c = b/c

Addition POE

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

Multiplication POE

If a=b, then a times c = b times c

CPCTC

Angle Side Angle Theorem

Angle Angle Side Theorem

Side Side Side Postulate

Corresponding parts of congruent triangles are congruent-- use…

If two angles and the included side of one triangle are congru…

If two angles and a non-included side of one triangle are cong…

If three sides of one triangle are congruent to three sides of…

CPCTC

Corresponding parts of congruent triangles are congruent-- use…

Angle Side Angle Theorem

If two angles and the included side of one triangle are congru…

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…

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

If a transversal intersects two parallel lines, then alternate…

If a transversal intersects two parallel lines, then correspon…

If a transversal intersects two parallel lines, the the Altern…

Postulate 3-1: Same Side Interior Angle…

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

Theorem 3-1: Alternate Interior Angles…

If a transversal intersects two parallel lines, then alternate…

Side-Side-Side (SSS) Congruence

Side-Angle-Side (SAS) Congruence

Angle-Side-Angle (ASA) Congruence

Angle-Angle-Side (AAS) Congruence

If three sides of one triangle are congruent to three sides of…

If two sides and the included angle of one triangle are congru…

If two angles and the included side of one triangle are congru…

If two angles and the non-included side of one triangle are co…

Side-Side-Side (SSS) Congruence

If three sides of one triangle are congruent to three sides of…

Side-Angle-Side (SAS) Congruence

If two sides and the included angle of one triangle are congru…

Midpoint Therum

Definition of Angle Bisector

Angle Bisector Theorem

Same Side Interior Angles Postulate

If M is the midpoint of line segment AB, then AM=1/2 AB and MB…

If ray BX is a bisects of <ABC, m<1=m<2

If ray BX is a bisector of <ABC, then m<ABX=1/2 m<ABC

If 2 lines are parallel and are cut by a transversal, then the…

Midpoint Therum

If M is the midpoint of line segment AB, then AM=1/2 AB and MB…

Definition of Angle Bisector

If ray BX is a bisects of <ABC, m<1=m<2

Postulate 1-1

Postulate 1-2

Postulate 1-3

Postulate 1-4

Through any two points there is exactly one line. (p.18)

If two lines intersect, then they intersect in exactly one poi…

Postulate If two planes intersect, then they intersect in exac…

Through any three noncollinear points there is exactly one pla…

Postulate 1-1

Through any two points there is exactly one line. (p.18)

Postulate 1-2

If two lines intersect, then they intersect in exactly one poi…

The Trichotomy ("Three Possibilities")…

The Transitive Property

The Addition Property of Inequality

The Multiplication Property of Inequali…

Either a>b, a=b, or a<b

If a>b and b>c, then a>c

If a>b, then a+c>b+c

If a>b and c>0, then ac>bc

The Trichotomy ("Three Possibilities")…

Either a>b, a=b, or a<b

The Transitive Property

If a>b and b>c, then a>c

Parallel Lines

Perpendicular Lines

Skew Lines

Parallel Planes

Are coplanar lines and do not intersect.

Lines that intersect at 90 degree angles.

Lines that are not coplanar, not parallel, and do not intersec…

Are planes that do not intersect.

Parallel Lines

Are coplanar lines and do not intersect.

Perpendicular Lines

Lines that intersect at 90 degree angles.

Postulate 1: Ruler Postulate

Postulate 2: Segment Addition Postulate

Postulate 3: Protractor Postulate

Postulate 4: The Angle Addition Postula…

The points on a line can be paired in a one-to-one corresponde…

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

Given a point X on line PR, consider rays XP and XR, as well a…

If point D is in the interior of Angle ABC, then the measureme…

Postulate 1: Ruler Postulate

The points on a line can be paired in a one-to-one corresponde…

Postulate 2: Segment Addition Postulate

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

segment addition postulate

angle addition postulate

linear pair theorem

congruent supplements theorem

If a point (c) is between two points (a and b), then ac+cb= ab.

If a point (d) is in the interior of angle <ABC, then <ABD + <…

If two angles are supplementary to the same angle, then they a…

If two angles are supplementary to the same angle, then they a…

segment addition postulate

If a point (c) is between two points (a and b), then ac+cb= ab.

angle addition postulate

If a point (d) is in the interior of angle <ABC, then <ABD + <…

perpendicular

parallel

point

line

two lines that intersect and form a right angle and have oppos…

two lines that have the same slope and never intersect or touch

an exact location in space

set of points that extends indefinitely

perpendicular

two lines that intersect and form a right angle and have oppos…

parallel

two lines that have the same slope and never intersect or touch

parallel lines

perpendicular lines

skew lines

parallel planes

coplanar lines that do not intersect

Lines that intersect to form right angles

lines that are noncoplanar, not parallel, and they do not inte…

planes that do not intersect

parallel lines

coplanar lines that do not intersect

perpendicular lines

Lines that intersect to form right angles

definition of linear pair

definition of segment bisector

definition of a right angle

segment addition postulate

Two adjacent angles whose sum is 180.

intersects the segment at its midpoint

an angle that measures 90 degrees.

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

definition of linear pair

Two adjacent angles whose sum is 180.

definition of segment bisector

intersects the segment at its midpoint

Parallelograms- About Sides

Parallelograms- About Angles

Parallelograms- About Diagonals

Parallelogram Converses- About Sides

If a quadrilateral is a parallelogram, the opposite... sides are…

* If a quadrilateral is a parallelogram, the opposite... angles…

* If a quadrilateral is a parallelogram, the diagonals... bisect…

* If both pairs of opposite sides of a quadrilateral... are para…

Parallelograms- About Sides

If a quadrilateral is a parallelogram, the opposite... sides are…

Parallelograms- About Angles

* If a quadrilateral is a parallelogram, the opposite... angles…

Postulate 2.1

Postulate 2.2

Postulate 2.3

Postulate 2.4

Through any two points, there is exactly one line.

Through any three noncollinear points, there is exactly one pl…

A line contains at least two points.

A plane contains at least three noncollinear points.

Postulate 2.1

Through any two points, there is exactly one line.

Postulate 2.2

Through any three noncollinear points, there is exactly one pl…

coplanar, do not intersect

equidistant

do not intersect

noncoplanar, do not intersect

Two lines are parallel iff they are ____ and __ ___ ____

Two lines are parallel iff they are everywhere ____

Two planes are parallel iff they _____ ____

Two lines are skew iff they are ____ and they __ ___ _____

coplanar, do not intersect

Two lines are parallel iff they are ____ and __ ___ ____

equidistant

Two lines are parallel iff they are everywhere ____

triangle sum theorem

exterior angles theorem

corollary to the triangle sum theorem

third angles theorem

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

the measure of an exterior angle of a triangle is equal to the…

the acute angles of a right triangle are complementary

if two angles of one triangle are congruent tot two angles of…

triangle sum theorem

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

exterior angles theorem

the measure of an exterior angle of a triangle is equal to the…

Segment Addition Postulate

Angle Addition Postulate

Through any two points there exists...

A line contains...

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

If P is in the interior of <RST, then m<RSP + m<PST = m<RST

...one line

...At least two points

Segment Addition Postulate

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

Angle Addition Postulate

If P is in the interior of <RST, then m<RSP + m<PST = m<RST

Two angles whose measures add to 90 deg…

Two angels whose measures add to 180 de…

Middle of a line segment that divides t…

A ray beginning at the vertex of an ang…

What are complementary angles?

What are supplementary angles?

What is a midpoint?

What is an angle bisector?

Two angles whose measures add to 90 deg…

What are complementary angles?

Two angels whose measures add to 180 de…

What are supplementary angles?