# Study sets matching "geometry 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…

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…

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…

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

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…

Postulate 2.1

Postulate 2.2

Postulate 2.3

Postulate 2.4

Through any two points, there is exactly one line.

Through any three points not on the same line, there is exactl…

...

...

Postulate 2.1

Through any two points, there is exactly one line.

Postulate 2.2

Through any three points not on the same line, there is exactl…

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

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

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

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…

Properties of Triangle Congruence

Properties of Segment Congruence Theorem

Properties of Angle Congruence Theorem

Right Angles Congruence Theorem

Triangle congruence is reflexive, symmetric, and transitive.

Segment congruence is reflexive, symmetric, and transitive.

Angle congruence is reflexive, symmetric, and transitive.

All right angles are congruent.

Properties of Triangle Congruence

Triangle congruence is reflexive, symmetric, and transitive.

Properties of Segment Congruence Theorem

Segment congruence is reflexive, symmetric, and transitive.

theorem 4-1

theorem 4-2

corollary 1

corollary 2

if 2 sides of a triangle are congruent, then the angles opposi…

if 2 angles of a triangle are congruent, then the sides opposi…

an equilateral triangle is also equalangular

an equilateral triangle has three 60 degree angles

theorem 4-1

if 2 sides of a triangle are congruent, then the angles opposi…

theorem 4-2

if 2 angles of a triangle are congruent, then the sides opposi…

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…

Postulate 1.1-1

Postulate 1.1-2

Postulate 1.1-3

Postulate 1.1-4

Through any two points there is exactly one line

Through any three noncollinear points there is exactly one pla…

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

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

Postulate 1.1-1

Through any two points there is exactly one line

Postulate 1.1-2

Through any three noncollinear points there is exactly one pla…

IF TWO LINES ARE PERPENDICULAR,

IF TWO LINES INTERSECT,

IN A PLANE,

IF TWO LINES MEET TO FORM A RIGHT ANGLE

...then they meet to form right angles

...then the vertical angles formed are congruent

... there is exactly one line perpendicular to a given line at…

...then these lines are perpendicular

IF TWO LINES ARE PERPENDICULAR,

...then they meet to form right angles

IF TWO LINES INTERSECT,

...then the vertical angles formed are congruent

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…

Ruler Postulate

Segment Addition Postulate

Protractor Postulate

Angle Addition Postulate

Using a Ruler for Construction

Adding 2 or more segments together.... ex.) AB + BC = AC

Using a Protractor to measure angles

Adding 2 or more Angles together... ex.) mAngleBAC = mAngle1 + m…

Ruler Postulate

Using a Ruler for Construction

Segment Addition Postulate

Adding 2 or more segments together.... ex.) AB + BC = AC

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 in…

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

on ab in a given plane, choose any point o between a and b. co…

if point b lies in the interior of <aoc, then m<aob + m<boc =…

postulate 1 - ruler postulate

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

postulate 2 - segment addition postulate

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

2.1: Points, Lines, and Planes Postulate

2.2: Points, Lines, and Planes Postulate

2.3: Points, Lines, and Planes Postulate

2.4: Points, Lines, and Planes Postulate

Through any two points, there is exactly one line

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

A line contains at least two points

A plane contains at three non-collinear points

2.1: Points, Lines, and Planes Postulate

Through any two points, there is exactly one line

2.2: Points, Lines, and Planes Postulate

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

ruler postulate

segment addition postulate

angle addition postulate

linear pair 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=AB . If AB+BC=AB, then B i…

if P is in the interior of angle RST, then the measure of angl…

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

ruler postulate

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

segment addition postulate

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

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

Perpendicular Transversal Theorem

Lines Perpendicular to a Transversal Th…

6 Vertical Angles Congruence Theorem

Parallel Postulate

If a transversal is perpendicular to one of two parallel lines…

In a plane, if two lines are perpendicular to the same line, t…

Vertical Angles are congruent.

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

Perpendicular Transversal Theorem

If a transversal is perpendicular to one of two parallel lines…

Lines Perpendicular to a Transversal Th…

In a plane, if two lines are perpendicular to the same line, t…

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 +…

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