# Study sets matching "geometry theorems corollaries"

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

If point B lies in the interior of <AOC…

If two parallel lines are cut by a tran…

If two lines are cut by a transversal a…

Segment Addition Postulate

Angle Addition Postulate

n is parallel to m

<1 is congruent to <2

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

Segment Addition Postulate

If point B lies in the interior of <AOC…

Angle Addition Postulate

Classifying Triangles by Sides

Classifying Triangles by Angles

(Theorem 5.1) Triangle Sum Theorem

(Theorem 5.2) Exterior Angle Theorem

SCALENE: no congruent sides... ISOSCELES: at least 2 congruent si…

ACUTE: 3 acute angles... RIGHT: 1 right angle... OBTUSE: 1 obtuse an…

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…

Classifying Triangles by Sides

SCALENE: no congruent sides... ISOSCELES: at least 2 congruent si…

Classifying Triangles by Angles

ACUTE: 3 acute angles... RIGHT: 1 right angle... OBTUSE: 1 obtuse an…

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…

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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…

Pythagorean Theorem

Triangle Sum Theorem

Betweeness of Points Theorem

Betweeness of Rays Theorem

a^2+b^2=c^2

The sum of the angles of a triangle is 180 degrees

If A-B-C, then AB+BC=AC

if OA-OB-OC, then angle AOB+ angle BOC= angle AOC

Pythagorean Theorem

a^2+b^2=c^2

Triangle Sum Theorem

The sum of the angles of a triangle is 180 degrees

Polygon interior angles theorem

Corollary to the polygon interior angle…

Polygon exterior angles theorem

Paralellogram opposite sides theorem

The sum of the measures of the interior angles of a convex n-g…

The sum of the measures of the interior angles of a quadrilate…

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

If a quadrilateral is a parallelogram, then it's opposite side…

Polygon interior angles theorem

The sum of the measures of the interior angles of a convex n-g…

Corollary to the polygon interior angle…

The sum of the measures of the interior angles of a quadrilate…

Linear Pair Theorem

Congruent Supplements Theorem

Congruent Complements Theorem

Vertical Angles Theorem

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

If two angles are supplementary to the same angle (or to 2 con…

If two angles are complementary to the same angle (or to 2 con…

If two angles are vertical angles, then they are congruent.

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 2 con…

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…

Corresponding Angles Postulate

Alternate Interior Angles Theorem

Alternate Exterior Angles Theorem

Same-Side Interior AngleTheorem

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

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

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

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

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 that pairs…

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…

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

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…

Triangle Proportionality Theorem

Converse of the Triangle Proportionally…

Two-Transversal Proportionality

Triangle Angle Bisector Theorem

If a line parallel to a side of a triangle intersects the othe…

If a line divides two sides of a triangle proportionally, then…

If three or more parallel lines intersect two transversals, th…

An angle bisector of a triangle divides the opposite side into…

Triangle Proportionality Theorem

If a line parallel to a side of a triangle intersects the othe…

Converse of the Triangle Proportionally…

If a line divides two sides of a triangle proportionally, then…

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

Postulate 1-1-1

Postulate 1-1-2

Post 1-1-3

Post 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 at 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…

THM 2-1/ MIDPOINT THM

THM 2-2/ ANGLE BISECTOR THM

THM 2-3

THM 2-4

If M is the midpoint of AB, then:... AM = 1/2AB and MB = 1/2AB

If BX is the bisector of ABC, then: mABX = 1/2mABC and mXBC =…

Vertical angles are congruent

If two lines are perpendicular, then they form congruent adjac…

THM 2-1/ MIDPOINT THM

If M is the midpoint of AB, then:... AM = 1/2AB and MB = 1/2AB

THM 2-2/ ANGLE BISECTOR THM

If BX is the bisector of ABC, then: mABX = 1/2mABC and mXBC =…

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…

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Theorem 16

Theorem 17

Corollary 1

Corollary 2

In a plane, two points each equidistant from the endpoint of a…

Equal corresponding angles means that lines are parallel

Equal alternative interior angles means lines are parallel

Supplementary angles on the same side of a transversal means t…

Theorem 16

In a plane, two points each equidistant from the endpoint of a…

Theorem 17

Equal corresponding angles means that lines are parallel

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…

Postulate 2.1

Postulate 2.2

Postulate 2.3

Postulate 2.4

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 least three non collinear points.

Postulate 2.1

Through any two points, there is exactly one line.

Postulate 2.2

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

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…