# Study sets matching "postulates geometry math theorems corollaries"

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Postulate 1.1

Postulate 1.2

Postulate 1.3

Postulate 1.4

Through any 2 points there is exactly one line.

If two lines intersect then they intersect at exactly one poin…

If two planes intersect then they intersect at exactly one lin…

Through any 3 Non-Collinear points there is exactly one plane.

Postulate 1.1

Through any 2 points there is exactly one line.

Postulate 1.2

If two lines intersect then they intersect at exactly one poin…

Exterior angle inequality thm

Addition prop of inequality

Subtraction prop of inequality

Multiplication prop of inequality

the meas. of an ext. angle of a triangle is > than either remo…

If a > b and c > or = to d, then a + c > b + d

If a > b and c = d, or if c = d and a > b, then a - c > b - d,…

If a > b and c > 0, then ca > cb... If a > b and c < 0, then ca <…

Exterior angle inequality thm

the meas. of an ext. angle of a triangle is > than either remo…

Addition prop of inequality

If a > b and c > or = to d, then a + c > b + d

Theorem 5.3 (Circumcenter Theorem)

Theorem 5.4 (Angle Bisector Theorem)

Theorem 5.5 (Converse of the Angle Bise…

Theorem 5.6 (Incenter Theorem)

The perpendicular bisectors of a triangle intersect at a point…

If a point is on the bisectors of an angle, then it is equidis…

If a point in the interior of an angle is equidistant from the…

The angle bisectors of a triangle intersect at a point called…

Theorem 5.3 (Circumcenter Theorem)

The perpendicular bisectors of a triangle intersect at a point…

Theorem 5.4 (Angle Bisector Theorem)

If a point is on the bisectors of an angle, then it is equidis…

Side-Side-Side (SSS)

Side-Angle-Side (SAS)

Angle-Side-Angle (ASA)

Angle-Angle-Side (AAS)

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

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

If two sides and the included side of one triangle are congrue…

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

Side-Side-Side (SSS)

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

Side-Angle-Side (SAS)

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

A point on the perpendicular bisector o…

A point equidistant from the endpoints…

A point on the bisector of an angle is

A point on or in the interior of an ang…

equidistant from the endpoints of the segments

perpendicular bisector of the segement

equidistant from the sides of the angle

sides of an angle lies on the bisector of the angle

A point on the perpendicular bisector o…

equidistant from the endpoints of the segments

A point equidistant from the endpoints…

perpendicular bisector of the segement

Segment Addition Postulate

Angle Addition Postulate

Pythagorean Theorem

Linear Pair Theorem

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

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

In a right triangle, the sum of the squares if the lengths of…

If two angles form a linear pair then they are supplementary

Segment Addition Postulate

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

Angle Addition Postulate

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

Polygon Exterior Angle Corollary

Quadrilateral Exterior Angle Sum Coroll…

Quadrilateral Interior Angle Sum Coroll…

Regular Polygon Interior Angle Corollary

the measure of each exterior and of a regular polygon of n sid…

the sum of the four exterior angles of a quadrilateral is 360°

the sum of the four interior angles of a quadrilateral is 360°

the measure of each interior angle of a regular polygon of n s…

Polygon Exterior Angle Corollary

the measure of each exterior and of a regular polygon of n sid…

Quadrilateral Exterior Angle Sum Coroll…

the sum of the four exterior angles of a quadrilateral is 360°

Linear Pair Postulate

Corresponding Angles Postulate

Two Perps Theorem

Perpendicular Transversal Theorem

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

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

If two lines are perpendicular to the same line, then the line…

If a line is perpendicular to one of two parallel lines, then…

Linear Pair Postulate

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

Corresponding Angles Postulate

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

linear pair theorem

congruent supplements theorem

right angle congruence theorem

congruent complements theorem

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

if two angles are supplementary to the same angle, then the tw…

all right angles are congruent

if two angles are complementary to the same angle, then the tw…

linear pair theorem

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

congruent supplements theorem

if two angles are supplementary to the same angle, then the tw…

Corollaries

Corollaries

Corollaries

Supplementary Angle Theorem

If two angles of one triangle are congruent to two angles of a…

Each angle of an equiangular triangle measures sixty degrees

In a triangle there can be at most one right angle or one obtu…

All angles which are supplementy to the same or equal angles a…

Corollaries

If two angles of one triangle are congruent to two angles of a…

Corollaries

Each angle of an equiangular triangle measures sixty degrees

If two angles of one triangle are congr…

Each angle of an equiangular triangle m…

In a triangle there can be at most

Supplementary Angle Theorem

then the third angles are congruent too

sixty degrees

one right angle or one obtuse angle

All angles which are supplementy to the same or equal angles a…

If two angles of one triangle are congr…

then the third angles are congruent too

Each angle of an equiangular triangle m…

sixty degrees

ruler postulate

segment addition postulate

protractor postulate

angle addition postulate

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

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

ruler postulate w angles

if point B lies in the interior of ∠AOC than m∠AOB + m∠BOC = m…

ruler postulate

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

segment addition postulate

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

Postulate 2 Segment Addition Postulate

Postulate 3

Postulate 4 Protractor Postulate

Postulate 5 Angle Addition Postulate

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

Any segment has exactly one midpoint

In a given plane, select any line AB and any point C between A…

If D is in the interior of angle ABC, then m angle ABC = m ang…

Postulate 2 Segment Addition Postulate

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

Postulate 3

Any segment has exactly one midpoint

Post 1-1-1

Post 1-1-2

Post 1-1-3

Post 1-1-4

Through any two points there is exactly one line

Through any three non-collinear points there is exactly one pl…

If two points lie in a plane, then the line containing those p…

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

Post 1-1-1

Through any two points there is exactly one line

Post 1-1-2

Through any three non-collinear points there is exactly one pl…

linear pair theorem

congruent supplements theorem

right angle congruence theorem

congruent complements theorem

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

if two angles are supplementary to the same angle (or to two c…

all right angles are congruent

if two angles are complementary to the same angle (or to two c…

linear pair theorem

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

congruent supplements theorem

if two angles are supplementary to the same angle (or to two c…

Corresponding angles postulate

alternate interior angles theorem

Alternate exterior angles theorem

Consecutive Interior Angles theorem

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

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

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

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

Corresponding angles postulate

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

alternate interior angles theorem

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

Through any two points, how many lines…

Through any 3 noncolinear points, how m…

If 2 points lie in a plane, does the th…

How many points do 2 lines intersect at?

Through any two points there is exactly one line

Through any 3 noncollinear points, there is exactly one plane…

If 2 points lie in a plane, then the line containing those poi…

If 2 lines intersect, then they intersect in exactly 1 point

Through any two points, how many lines…

Through any two points there is exactly one line

Through any 3 noncolinear points, how m…

Through any 3 noncollinear points, there is exactly one plane…

Congruent

congruent segments

midpoint of a segment

bisector of a segment

two objects that have the same size and shape

segments that have equal lengths

point that divides the segment into 2 congruent segments

a line, a segment, ray, or plane that intersects the segment a…

Congruent

two objects that have the same size and shape

congruent segments

segments that have equal lengths

postulate 5

postulate 6

postulate 7

postulate 8

through any two points there exists exactly one line

a line contains at least two points

if two distinct lines intersect, then their intersection is ex…

through any 3 non-collinear points there exists exactly one pl…

postulate 5

through any two points there exists exactly one line

postulate 6

a line contains at least two points

Segment Addition P

Protractor P

Angle Addition P

Pythagorean T

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

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

If S in the interior of angle PQR, then the measure of angle P…

In a right triangle, the sum of the squares of the lengths of…

Segment Addition P

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

Protractor P

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

Through any two points there is

Through any three noncollinear points t…

If two points lie on a plane, then the…

Ruler Postulate

exactly one line

one plane containing them

lies in the plane

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

Through any two points there is

exactly one line

Through any three noncollinear points t…

one plane containing them

Segment Addition Postulate

Angle Addition Postulate

Point Number Postulate

Line Postulate

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 =…

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

Through any two points there is exactly one line.

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 =…

Postulate 1 (Ruler Postulate)

Postulate 2 (Segment Addition Postulate)

Postulate 3 (Protractor Postulate)

Postulate 4 (Angle Addition Postulate)

1. The points on a line can be paired with the real numbers 0…

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

On line AB in a given line, choose any point O between A and B…

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

Postulate 1 (Ruler Postulate)

1. The points on a line can be paired with the real numbers 0…

Postulate 2 (Segment Addition Postulate)

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

Postulate 1

Postulate 2:

Postulate 3:

Postulate 4:

Ruler Postulate: The points on a line can be paired in a one t…

Segment Addition Postulate:... If B is between A and C, then AB +…

Protractor Postulate:... Given a point, X, on line PR, consider…

Angle Addition Postulate:... If point D is in the interior of <AB…

Postulate 1

Ruler Postulate: The points on a line can be paired in a one t…

Postulate 2:

Segment Addition Postulate:... If B is between A and C, then AB +…

Right Angles Congruence Theorem

Midpoint Theorem

Ruler Postulate

Segment Addition Postulate

All right angles are congruent

If M is the midpoint of line segment AB, then line segment AM…

Given any 2 points A and B on a line, if A corresponds to 0, t…

If A, B, and C are collinear and AB+BC=AC, then B is between p…

Right Angles Congruence Theorem

All right angles are congruent

Midpoint Theorem

If M is the midpoint of line segment AB, then line segment AM…