#### Study sets matching "postulates geometry theorems"

#### Study sets matching "postulates geometry theorems"

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 o…

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

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

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

Side-Side-Side (SSS) Congruence

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

Side-Angle-Side (SAS) Congruence

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

Corresponding Angles

Corresponding Angles Converse

Alternate Interior Angles

Alternate Exterior Angles

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

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

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

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

Corresponding Angles

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

Corresponding Angles Converse

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

Radius

Chords

Tangents

Arcs

In a circle, a radius perpendicular to a chord bisects the ch…

In a circle, or congruent circles, congruent chords are equid…

Tangent segments to a circle from the same external point are…

In the same circle, or congruent circles, congruent central a…

Radius

In a circle, a radius perpendicular to a chord bisects the ch…

Chords

In a circle, or congruent circles, congruent chords are equid…

Expansion Postulate

Line Postulate

Plane Postulate

Flat Plane Postulate

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

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…

Expansion Postulate

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

Line Postulate

Any two points in space lie in 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 di…

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

undefined term

a word without a formal definition

point

undefined, a location with no size or dimension

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

there is exactly one line.

there is exactly one plane.

two points.

three noncollinear points.

Through any two points,

Through any three noncollinear points,

A line contains at least

A plane contains at least

there is exactly one line.

Through any two points,

there is exactly one plane.

Through any three noncollinear points,

theorem

postulate

definition

segment bisector

a statement that can be proved

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

assigns a term to an object. are always reversible

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

theorem

a statement that can be proved

postulate

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

Parallelograms- About Sides

Parallelograms- About Angles

Parallelograms- About Diagonals

Parallelogram Converses- About Sides

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

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

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

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

Parallelograms- About Sides

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

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 p…

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 p…

Postulate 1

Postulate 4

Postulate 5

Postulate 6

(Segment Addition Postulate)... if B is between A and C, then AB…

(Angle Addition Postulate)... if B lies in the interior of <AOC,…

a LINE contains at least 2 POINTS... a PLANE contains at least 3…

through any 2 POINTS there is exactly 1 LINE

Postulate 1

(Segment Addition Postulate)... if B is between A and C, then AB…

Postulate 4

(Angle Addition Postulate)... if B lies in the interior of <AOC,…

Ruler Postulate

Segment Addition Postulate

Protractor Postulate

Angle Addition Postulate

The points on a line can be put into a one-to-one corresponde…

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

Given AB and a point O on AB, all rays that can be drawn from…

If S is in the interior of PQR, then PQS+SQR=PQR

Ruler Postulate

The points on a line can be put into a one-to-one corresponde…

Segment Addition Postulate

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

Angle Addition Postulate

Segment Addition Postulate

Pythagorean Theorem

Linear Pair Theorem

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

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

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

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. (ba…

Segment Addition Postulate

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

Reflexive property

Symmetric property

Transitive property

Addition postulate

A quantity is congruent to itself

If a=b then b=a

If a=b and b=c then a=c

If equal quantities are added to equal quantities the sums ar…

Reflexive property

A quantity is congruent to itself

Symmetric property

If a=b then b=a

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 congr…

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

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 congr…

Postulate 1

Postulate 2

Postulate 3

Postulate 4

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

Through any 2 points there is exactly one line.

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

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

Postulate 1

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

Postulate 2

Through any 2 points there is exactly one line.

Postulate 5

Postulate 6

Postulate 7

Postulate 8

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

Through any two points there is exactly one line

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

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

Postulate 5

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

Postulate 6

Through any two points there is exactly one line

Ruler Postulate

Segment Addition Postulate

Protractor Postulate

Angle Addition Postulate

the points on a line can be put into one-to-one correspondenc…

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

Given line AB and point O on line AB, all rays that can be dr…

If S is in the interior of M<PQR + M<SQR = m<PQR

Ruler Postulate

the points on a line can be put into one-to-one correspondenc…

Segment Addition Postulate

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

Segment addition postulate

Angle addition postulate

Definition of midpoint

Definition of angle bisector

If Q is between P and R, then PR + QR = PR

If F is the interior of angle CDE, then angle CDF + angle FDE…

A segment or point that bisects a segment into two congruent…

A segment or point that bisects an angle into two congruent a…

Segment addition postulate

If Q is between P and R, then PR + QR = PR

Angle addition postulate

If F is the interior of angle CDE, then angle CDF + angle FDE…

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 trans…

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

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

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 trans…

Postulate 1:

Postulate 2:

Postulate 3:

Postulate 4:

Through any 2 points there is exactly 1 line

Through any 3 non - collinear points, there is exactly 1 plane

If 2 lines cross, they cross only once at a point

If 2 planes cross, the cross once at a line

Postulate 1:

Through any 2 points there is exactly 1 line

Postulate 2:

Through any 3 non - collinear points, there is exactly 1 plane

Logic

If orThen

Original Statement

Converse

the principles that guide reasoning within a given field or s…

100% must be true (math, science,...)

if A, then B (must B true)

If B, then A (could B true)

Logic

the principles that guide reasoning within a given field or s…

If orThen

100% must be true (math, science,...)

Law Of Detachment

Law Of Syllogism

Linear Pair Theorem

Congruent Supplements Theorem

If P>Q is a true statement and P is true, then Q is true

If P>Q and Q>R are true statements, then P>R is a true statem…

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

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

Law Of Detachment

If P>Q is a true statement and P is true, then Q is true

Law Of Syllogism

If P>Q and Q>R are true statements, then P>R is a true statem…

Segment addition postulate

Angle addition postulate

Linear pair postulate

Addition property

If three points A, B and C are collinear, and B is between A…

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

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

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

Segment addition postulate

If three points A, B and C are collinear, and B is between A…

Angle addition postulate

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