# Study sets matching "geometry theorems postulates"

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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…

Corresponding Angles

Corresponding Angles Converse

Alternate Interior Angles

Alternate Exterior Angles

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

If two lines are cut by a transversal and the corresponding an…

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

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

Corresponding Angles

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

Corresponding Angles Converse

If two lines are cut by a transversal and the corresponding an…

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…

Conditional

Converse

Inverse

Contrapositive

p→q; if p then q; equivalent to Contrapositive

q→p; if q then p; equivalent to Inverse

~p→~q; if not p then not q; equivalent to Converse

~q→~p; if not q then not p; equivalent to Conditional

Conditional

p→q; if p then q; equivalent to Contrapositive

Converse

q→p; if q then p; equivalent to Inverse

Postulate 3-1 Same-side Interior Angle…

Theorem 3-1 Alternate Interior Angles T…

Theorem 3-2 Corresponding Angles Theore…

Theorem 3-3 Alternate Exterior Angles T…

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 T…

congruent

theorem

postulate

definition

segment bisector

a statement that can be proved

something we don't need to prove, uses past information to bas…

assigns a term to an object. are always reversible

segment,ray,line, plane that divides a segment into two congru…

theorem

a statement that can be proved

postulate

something we don't need to prove, uses past information to bas…

Angle addition postulate

Postulate

Postulate

postulate

M<AOB + M<BOC = M<AOC... Any angles added together

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 throu…

Angle addition postulate

M<AOB + M<BOC = M<AOC... Any angles added together

Postulate

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

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

Postulate 3-1 Same-side Interior Angle…

Theorem 3-1 Alternate Interior Angles T…

Theorem 3-2 Corresponding Angles Theore…

Theorem 3-3 Alternate Exterior Angles T…

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 T…

congruent

Postulate 1

Postulate 2

Postulate 3

Postulate 4

Ruler Postulate... 1.) the points on a line can be paired with t…

Segment addition postulate

Protractor Postulate

angle addition postulate

Postulate 1

Ruler Postulate... 1.) the points on a line can be paired with t…

Postulate 2

Segment addition postulate

Vertical Angles Theorem

Congruent Supplements Theorem

Congruent Complements Theorem

Congruent Right Angles Theorem

Vertical angles are congruent.

If two angles are supplements of the same angles (or of congru…

If two angles are complements of the same angles (or of congru…

All right angles are congruent.

Vertical Angles Theorem

Vertical angles are congruent.

Congruent Supplements Theorem

If two angles are supplements of the same angles (or of congru…

Postulate 5

Postulate 6

Postulate 7

Postulate 8

A line contains at least 2 points; a plane contains at least 3…

Through any two points there is exactly one line

Through any 3 points there is at least 1 plane, and through an…

If 2 points are in a plane, then the line that contains the po…

Postulate 5

A line contains at least 2 points; a plane contains at least 3…

Postulate 6

Through any two points there is exactly one line

Angle Addition Postulate

Segment Addition Postulate

Pythagorean Theorem

Linear Pair Theorem

If S is in the interior of PQR, then mPQS + mSQR = m PQR. (bas…

If B is between A & C, then AB + BC = AC. (basically means: 2…

In a right triangle, leg squared + leg squared = hypotenuse sq…

If two angles form a linear pair, then they are supplementary.

Angle Addition Postulate

If S is in the interior of PQR, then mPQS + mSQR = m PQR. (bas…

Segment Addition Postulate

If B is between A & C, then AB + BC = AC. (basically means: 2…

Postulate 1

Postulate 2

Postulate 3

Postulate 4

A line contains at least 2 points;... A plane contains at least 3…

Through any 2 points there is exactly one line.

Through any 3 points there is at least 1 plane, and through an…

If 2 points are a plane, then the line that contains the point…

Postulate 1

A line contains at least 2 points;... A plane contains at least 3…

Postulate 2

Through any 2 points there is exactly one line.

Segment addition postulate

Angle addition postulate

Through any two points

Through any three points there is at le…

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

If point B lies in the interior of angle AOC, then measurement…

Through any two points there is exactly one line

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

Segment addition postulate

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

Angle addition postulate

If point B lies in the interior of angle AOC, then measurement…

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.

Ruler Postulate

Segment Addition Postulate

Protractor Postulate

Angle Addition Postulate

the points on the line can be paired with the real numbers in…

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

To find the measure of an angle, compute the absolute value of…

If point B is in the interior of <AOC, then m<AOB + m<BOC = m<…

Ruler Postulate

the points on the line can be paired with the real numbers in…

Segment Addition Postulate

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

Points, Lines, and Planes Postulates (7)

Midpoint Theorem

Addition Property

Subtraction Property

- Through any two points there is exactly one line... - Through a…

If M is the midpoint of AB, then AM = MB

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

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

Points, Lines, and Planes Postulates (7)

- Through any two points there is exactly one line... - Through a…

Midpoint Theorem

If M is the midpoint of AB, then AM = MB

one plane is two points

two plane is 3 points

2 points on a line

3 points on a plane

Through any 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

one plane is two points

Through any points, there is exactly one line

two plane is 3 points

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

Definition of Supplementary Angles

Definition of Alternate Interior Angles

Definition of Alternate Exterior angles

Definition of Corresponding Angles

2 angles whose measures have a sum of 180 degrees

2 non-adjacent angles that lie on opposite sides of the transv…

2 angles who are on opposite sides of the transversal and outs…

2 angles who are on the same side of the transversal and the s…

Definition of Supplementary Angles

2 angles whose measures have a sum of 180 degrees

Definition of Alternate Interior Angles

2 non-adjacent angles that lie on opposite sides of the transv…

Postulate 1-1

Postulate 1-2

Postulate 1-3

Postulate 1-4

through any two points, there is exactly one line

if two distinct lines intersect, then they intersect in exactl…

if two distinct planes intersect, they intersect in exactly on…

through any three non-colinear points there is exactly one pla…

Postulate 1-1

through any two points, there is exactly one line

Postulate 1-2

if two distinct lines intersect, then they intersect in exactl…

Expansion Postulate

Line Postulate

Plane Postulate

Flat Plane Postulate

A line contains at least two points. A plane contains at least…

Any two points in space lie in exactly one line

Three distinct noncollinear points lie in exactly one plane

If two points lie in a plane, then the line containing these t…

Expansion Postulate

A line contains at least two points. A plane contains at least…

Line Postulate

Any two points in space lie in exactly one line