# 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…

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…

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

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…

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…

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

Two points are symmetric with respect t…

In a plane, two points each equidistant…

Equal corresponding angles

Equal alternate interior angles

iff the line is the perpendicular bisector of the line segment…

determine the perpendicular bisector of the line segment.

mean that lines are parallel.

mean that lines are parallel.

Two points are symmetric with respect t…

iff the line is the perpendicular bisector of the line segment…

In a plane, two points each equidistant…

determine the perpendicular bisector of the line segment.

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.

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

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…

Postulate 3.4

Postulate 3.5

Theorem 3.5

Theorem 3.6

If corresponding angles are congruent, then lines are parallel

If given a line and point not on the line, then there exists e…

If alternate exterior angles are congruent, then lines are par…

If same sided interior angles are congruent, then lines are pa…

Postulate 3.4

If corresponding angles are congruent, then lines are parallel

Postulate 3.5

If given a line and point not on the line, then there exists e…

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…

Opp sides ≅

Opp ∠'s ≅

‖ lines are equidistant at all pts

Consec ∠'s supp

In a parallelogram, opposite sides are congruent.

In a parallelogram, opposite angles are congruent.

If line a is parallel to line b, them a and b are equidistant…

In a parallelogram, angle A and angle B are supplementary and…

Opp sides ≅

In a parallelogram, opposite sides are congruent.

Opp ∠'s ≅

In a parallelogram, opposite angles are congruent.

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…

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…

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

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…

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

Polygon Angle Sum Theorem

Polygon Exterior Angle Sum Theorem

Properties of a Parallelogram

Conditions to prove that a quadrilatera…

The sum of the interior angle measures of a convex polygon wit…

The sum of the measures of the exterior angles of a convex pol…

If a quadrilateral is a parallelogram, then:... 1. its opposite…

1. If one pair of opposite sides of a quadrilateral are both p…

Polygon Angle Sum Theorem

The sum of the interior angle measures of a convex polygon wit…

Polygon Exterior Angle Sum Theorem

The sum of the measures of the exterior angles of a convex pol…

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…

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 =…