# Study sets matching "geometry theorems etc"

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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…

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…

Segment Addition Postulate

Angle Addition Postulate

Midpoint

segment bisector

if b is between a and c, then ab+bc=ac

if point B lies in the interior of <AOC, then m<AOB +m<BOC=m<A…

m is the midpoint of ab if and only if AM=MB

CD bisects AB if and only if M is the endpoint of AB

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 <AOC, then m<AOB +m<BOC=m<A…

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

Bisection point

Midpoint

Trisect

Bisect

A point (or segment, ray, or line) that divides a segment into…

the bisection point of a segment

to divide a segment into 3 congruent segments (or angles)

to divide a segment into 2 congruent segments (or angles)

Bisection point

A point (or segment, ray, or line) that divides a segment into…

Midpoint

the bisection point of a segment

Postulate 1 (Ruler Postulate)

Postulate 2 (Segment Addition Postulate)

Postulate 3 (Protractor Postulate)

Postulate 4 (Angle Addition Postulate)

The distance between points a and b is the absolute value of t…

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

The measure of angle AOB is equal to the absolute value of the…

If point B is in the interior of angle COA, then the measure o…

Postulate 1 (Ruler Postulate)

The distance between points a and b is the absolute value of t…

Postulate 2 (Segment Addition Postulate)

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

Addition Property of Equality

Subtraction Property of Equality

Multiplication Property of Equality

Division Property of Equality

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

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

If a = b, then a * c = b * c

If a = b and c ≠ 0, then a/c = b/c

Addition Property of Equality

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

Subtraction Property of Equality

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

Side-Angle-Side (SAS) (Postulate)

Side-Side-Side (SSS) (Postulate)

Angle-Side-Angle (Postulate)

Angle-Angle-Side (AAS) Theorem

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

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

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

If two angles and a non include side of one triangle are congr…

Side-Angle-Side (SAS) (Postulate)

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

Side-Side-Side (SSS) (Postulate)

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

Same-Side Interiors Angle Postulate

Alternate Interior Angles Theorem

Corresponding Angles Theorem

Alternate Exterior Angles Theorem

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

If a transversal intersects two parallel lines, the alternate…

If a transversal intersects two parallel lines, then correspon…

If a transversal intersects two parallel lines, then alternate…

Same-Side Interiors Angle Postulate

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

Alternate Interior Angles Theorem

If a transversal intersects two parallel lines, the alternate…

Addition property

Subtraction property

Multiplication property

Division property

If A=B and C=D, then a+c=b+d

If A=B and C=D, then a-c=b-d

If A=B, then CA=CB

If A=B, then C=0, then a/c=b/c

Addition property

If A=B and C=D, then a+c=b+d

Subtraction property

If A=B and C=D, then a-c=b-d

AA Similarity Postulate

SAS Similarity Theorem

SSS Similarity Theorem

Triangle Proportionality Theorem

If two angles of one triangle are congruent to two other trian…

If an angle of one triangle is congruent to an angle of anothe…

If the sides of two triangles are in proportion, then the tria…

If a line parallel to one side of a triangle intersects the ot…

AA Similarity Postulate

If two angles of one triangle are congruent to two other trian…

SAS Similarity Theorem

If an angle of one triangle is congruent to an angle of anothe…

isosceles triangle theorem

isosceles triangle converse

1 corollary

2 corollary

if two sides are congruent then the angles opp. the sides are…

if two angles are congruent then the sides opp. those angles a…

the acute angles of a right triangle are comp.

the measure of each angle of equiangular triangle is 60 degree…

isosceles triangle theorem

if two sides are congruent then the angles opp. the sides are…

isosceles triangle converse

if two angles are congruent then the sides opp. those angles a…

perpendicular lines

skew lines

Parallel planes

transversal

intersect at 90 degree angles

are not coplanar, parallel, and do not intersect

planes that do not intersect

a line that intersects to coplanar lines at two different poin…

perpendicular lines

intersect at 90 degree angles

skew lines

are not coplanar, parallel, and do not intersect

Posulate 5

Poatulate 6

Postulate 7

Postulate 8

Through any two points there exists exactly one line.

A line contains at least two points.

If two lines intersect, then their intersection is exactly one…

Through any three noncollinear points there exists exactly one…

Posulate 5

Through any two points there exists exactly one line.

Poatulate 6

A line contains at least two points.

Addition Postulate

Subtraction Postulate

Multiplication Postulate

Division Postulate

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

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

if a=b, then ac = bc

if a=b and c is not equal to 0, then a/c = b/c

Addition Postulate

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

Subtraction Postulate

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

triangle sum theorem

Exterior Angle 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 of two angles of a…

triangle sum theorem

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

Exterior Angle Theorem

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

Segment Addition Postulate

Midpoint formula

Distance formula

Angle Addition Postulate

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

(x₁+x₂)/2, (y₁+y₂)/2.

d = √[( x₂ - x₁)² + (y₂ - y₁)²].

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

Segment Addition Postulate

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

Midpoint formula

(x₁+x₂)/2, (y₁+y₂)/2.

Addition Property of Equality

Subtraction Property of Equality

Multiplication Property of Equality

Division Property of Equality

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

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

If a=b, then ca=cb

If a=b and c≠0, then a÷c=b÷c

Addition Property of Equality

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

Subtraction Property of Equality

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

Linear Pair Theorem

Theorem

Congruent supplements theorem

Right angle congruence theorem

If 2 angles form a linear pair, then they are supplementary

A statement that must be proven

If 2 angles are supplementary to the same angle, then the 2 an…

All right angles are congruent

Linear Pair Theorem

If 2 angles form a linear pair, then they are supplementary

Theorem

A statement that must be proven

Point

Name Points

Line

Name Lines

A location in space that has no dimension

Upper-case print letter is used to __.

A set of infinite points in one dimension;goes infinitely in b…

Using a lower-case cursive letter OR using a 2 points and a li…

Point

A location in space that has no dimension

Name Points

Upper-case print letter is used to __.

Definition of parallel lines

Definition of skew lines

Definition of parallel planes

If two parallel planes are cut by a thi…

Coplanar lines that do not intersect

Noncoplanar lines; neither parallel or intersecting

Non intersecting planes

The lines of intersection are parallel

Definition of parallel lines

Coplanar lines that do not intersect

Definition of skew lines

Noncoplanar lines; neither parallel or intersecting

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

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

If M is the midpoint of AB, then AM = ½…

If AD is the bisector of <CAB then m<BA…

Addition Property:

Subtraction Property:

Theorum 2-1: Midpoint Theorem

Theorum 2-2: Angle Bisector Theorem.

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

Addition Property:

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

Subtraction Property:

postulate

Segment Addition Postulate

acute angles

obtuse angles

an accepted statement of fact without proog

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

measure between 0 and 90 degrees

measure between 90 and 180

postulate

an accepted statement of fact without proog

Segment Addition Postulate

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