# Study sets matching "postulates geometry theorems"

Radius

Chords

Tangents

Arcs

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

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

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

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

Radius

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

Chords

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

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…

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…

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…

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 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.... (ba…

Segment Addition Postulate

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

Addition Prop. Of... equality

Subtraction Prop. Of... equality

Symmetric Property... of Equality

Transitive Property of... Equality

If the same number is added to equal... numbers, then the sums ar…

If the same number is subtracted from equal... numbers, then the…

If a = b then b = a

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

Addition Prop. Of... equality

If the same number is added to equal... numbers, then the sums ar…

Subtraction Prop. Of... equality

If the same number is subtracted from equal... numbers, then the…

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 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.... (ba…

Segment Addition Postulate

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

Segment Addition Postulate

Protractor Postulate

Angle Addition Postulate

Law of Detachment

Let A, B, and C be collinear points. If B is between A and C,…

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

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

if p->q is a true conditional statement, and p is true, then q…

Segment Addition Postulate

Let A, B, and C be collinear points. If B is between A and C,…

Protractor Postulate

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

1.1 Ruler Postulate

1.2 Segment Addition Postulate

1.3 Protractor Postulate

1.4 Angle Addition Postulate

The points on a line can be matched one to one with the real n…

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

Consider ⃖line OB⃗ and a point A on one side of line OB⃖⃗. The…

If P is in the interior of ∠RST, then the measure of ∠RST is e…

1.1 Ruler Postulate

The points on a line can be matched one to one with the real n…

1.2 Segment Addition Postulate

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

segment addition postulate

definition of a midpoint

angle addition postulate

definition of a bisector

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

a point that bisects/divides the segment into 2 congruent segm…

if S is in the interior of angle PQR then PQS+SQR=PQR

a ray that divides an angle into 2 congruent segments

segment addition postulate

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

definition of a midpoint

a point that bisects/divides the segment into 2 congruent segm…

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…

Segment congruence postulate

Segment addition postulate

Angle congruence postulate

Angle addition postulate

If two segements have the same length as measured by a fair ru…

If point R is between points P and Q on a line then; PR + RQ =…

If two angles have the same measure, then they are congruent.…

If point S is in the interior of angle PQR, then the measure o…

Segment congruence postulate

If two segements have the same length as measured by a fair ru…

Segment addition postulate

If point R is between points P and Q on a line then; PR + RQ =…

skew lines

postulate 13 - parallel postulate

postulate 14- perpendicular postulate

transversal

do not intersect an are not coplanar

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

If there is a line and a point on the line, then there is exac…

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

skew lines

do not intersect an are not coplanar

postulate 13 - parallel postulate

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

ruler postulate

segment addition postulate

protractor postulate

angle addition postulate

the distance between points A and B, written as AB, is the abs…

if B is between A and C, then AB+BC=AC. if AB+BC=AC, the B is…

the measure of ∠AOB, which can be written as m∠AOB, is equal t…

if b is in the interior of ∠COA, then m∠COA is equal to the su…

ruler postulate

the distance between points A and B, written as AB, is the abs…

segment addition postulate

if B is between A and C, then AB+BC=AC. if AB+BC=AC, the B is…

Conditional statements

Deductive Reasoning

Law of Detatchment

Segment Addition Postulate

a statement that can be written in if/then form "if you study…

uses facts, rules, and definitions

A form of inductive reasoning that is sued to draw conclusions…

segments on the same line add to the larger line

Conditional statements

a statement that can be written in if/then form "if you study…

Deductive Reasoning

uses facts, rules, and definitions

Ruler Postulate

Segment Addition Postulate

Protractor Postulate

Angle Addition Postulate

The points on a line can be paired with real numbers in such a…

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

On Line AB in a given plane, choose any point between A and B.…

If Point B lies in the interior of Angle AOC, then the measure…

Ruler Postulate

The points on a line can be paired with real numbers in such a…

Segment Addition Postulate

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

Postulate 1-2

Postulate 1-3

Postulate 1-4

Ruler Postulate

If 2 distinct lines intersect, then they intersect in exactly…

If 2 distinct planes intersect, then they intersect in exactly…

Through any three noncollinear points there is exactly one pla…

Every point on a line can be paired with a real number. This m…

Postulate 1-2

If 2 distinct lines intersect, then they intersect in exactly…

Postulate 1-3

If 2 distinct planes intersect, then they intersect in exactly…

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

Segment Addition Postulate

Alternate Interior Angles

Alternate Exterior Angles

Corresponding Angles Postulate

AB + BC = AC

a pair of angles between the two lines on alternate sides of t…

A pair of angles that are in the exterior and both on alternat…

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

Segment Addition Postulate

AB + BC = AC

Alternate Interior Angles

a pair of angles between the two lines on alternate sides of t…

Side-Side-Side Postulate... (SSS)

Side-Angle-Side Postulate... (SAS)

Angle-Side-Angle Postulate... (ASA)

Angle-Angle-Side Theorem... (AAS)

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

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 a non included side of one triangle are cong…

Side-Side-Side Postulate... (SSS)

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

Side-Angle-Side Postulate... (SAS)

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

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 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.... (ba…

Segment Addition Postulate-

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

point

line

plane

collinear points

spot;an object with no dimension

straight; an object that extends infinitely

flat;extends infinitely in two dimension

points that lie on the same line

point

spot;an object with no dimension

line

straight; an object that extends infinitely

Definition of Midpoint

Vertical Angles Theorem

Reflexive property

Symmetric property

(Not def. Of congruent segments)

∠CXE=∠CXE

GH = KL so ... KL = GH

Definition of Midpoint

(Not def. Of congruent segments)

Vertical Angles Theorem