# Study sets matching "geometry properties corollaries"

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Reflexive Property

Symmetric Property

Transitive Property

Substitution Postulate

Any quantity is equal/congruent to itself.

If a=b , then b=a . Same holds for congruence.

If a=b and b=c , then a=c . Same holds for congruence.

Any quantity can be substituted for its equal in any expressio…

Reflexive Property

Any quantity is equal/congruent to itself.

Symmetric Property

If a=b , then b=a . Same holds for congruence.

Postulate 1

Postulate 2

The Ruler Postulate

The Protractor Postulate

2 points determine a line

3 noncollinear points determine a plane

the points on a line can be numbered so that positive number d…

the rays in a half rotation can be numbered from 0 to 180 so t…

Postulate 1

2 points determine a line

Postulate 2

3 noncollinear points determine a plane

(Postulate 1)The Ruler Postulate

(Postulate 2) The Segment Addition Post…

(Postulate 3) The Protractor Postulate

(Postulate 4) The Angle Addition Postul…

On a number line, the distance between 2 pts. can be determine…

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

Angles have a measure between 0 degrees (Exclusive) and 180 de…

If point P is in the interior of ∠ABC, then ... m∠ABP + m∠PBC = m…

(Postulate 1)The Ruler Postulate

On a number line, the distance between 2 pts. can be determine…

(Postulate 2) The Segment Addition Post…

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

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theorem

addition property of equality

subtraction property of equality

multiplication property of equality

a statement that has been proven

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

is a=b, then a-c=b-c

is a=b, then ac=bc

theorem

a statement that has been proven

addition property of equality

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

Addition Property of Inequality (API)

Multiplication Property of Inequality (…

Division Property of Inequality (DPI)

Transitive Property of Inequality (TPI)

If a>b and c≥d, then a+c>b+d

If a>b and c>0, then ac>bc... and... If a>b and c<0, then ac<bc

If a>b and c>0, then a/c>b/c... and... If a>b and c<0, then a/c<b/c

If a>b and b>c, then a>c

Addition Property of Inequality (API)

If a>b and c≥d, then a+c>b+d

Multiplication Property of Inequality (…

If a>b and c>0, then ac>bc... and... If a>b and c<0, then ac<bc

Point

Line

Line Segment

Plane

Does not have any size or shape; Used to identify a location

Extends forever in two directtions; There is no infinite numbe…

A line connected by two endpoints

Extends forever with no thickness; Must have at least 3 points

Point

Does not have any size or shape; Used to identify a location

Line

Extends forever in two directtions; There is no infinite numbe…

If point D lies in between angle ABC, t…

If point B lies between A and C, then A…

AB=AB

If a=b then a+c=a+b, c-a=c-b, c/a=c/b,…

Angle Addition Postulate (both parts)

Segment Addition Postulate

Reflexive Property

Addition/Subtraction/Division/Multiplication Property of Equal…

If point D lies in between angle ABC, t…

Angle Addition Postulate (both parts)

If point B lies between A and C, then A…

Segment Addition Postulate

if 2 angles of one triangle are congrue…

____ the third angles are congeuent

what are the measures of the angles of…

how many obtuse or right angles can be…

the third angles are congruent

if 2 angles of one triangle are congruent to two angles of ano…

each angle of an equiangular triangle has measure 60

in a triangle, there can be at most one right angle or obtuse…

if 2 angles of one triangle are congrue…

the third angles are congruent

____ the third angles are congeuent

if 2 angles of one triangle are congruent to two angles of ano…

Segment Addition Postulate

Angle Addition Postulate

How many points does a line contain? Ho…

How many planes are through any 3 point…

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

If a ray lies in the interior of an angle, then the 2 angles t…

2, 3, 4

At least 1, exactly 1

Segment Addition Postulate

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

Angle Addition Postulate

If a ray lies in the interior of an angle, then the 2 angles t…

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 pl…

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 pl…

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°

AA (Angle-Angle) Similarity Postulate

SSS (Side-Side-Side) Triangle Similarit…

SAS (Side-Angle-Side) Triangle Similari…

Side-Splitter Theorem

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

If the corresponding sides of two triangles are proportional,…

If an angle of one triangle is congruent to an angle of a seco…

If a line is parallel to one side of a triangle and intersects…

AA (Angle-Angle) Similarity Postulate

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

SSS (Side-Side-Side) Triangle Similarit…

If the corresponding sides of two triangles are proportional,…

Postulate

Basic Postulates of Geometry

Angle Addition Postulate

Linear Pair Postulate

"Common sense rules" based on other definitions.

The intersection of two lines is a point.... How many points det…

If an angle is split by another ray, then the two parts add up…

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

Postulate

"Common sense rules" based on other definitions.

Basic Postulates of Geometry

The intersection of two lines is a point.... How many points det…

Determinance Postulate 1

Ruler Postulate

Segment Addition Postulate

Intersection Postulate 1

Through two points, there is exactly one line

The measure of any line segment is a unique positive number

If X is a point on line segment AB, and is between points A an…

If two lines intersect, their intersection is exactly one point

Determinance Postulate 1

Through two points, there is exactly one line

Ruler Postulate

The measure of any line segment is a unique positive number

Before Studying, please change the opti…

In a right triangle, the sum of the squ…

If 2 angles are vertical angles, then t…

Perpendicular lines intersect to form 4…

Thank you. :)

Pythagorean Theorem (Chapter 1)

State the Theorem:(Chapter 1)

State the Theorem:(Chapter 1)

Before Studying, please change the opti…

Thank you. :)

In a right triangle, the sum of the squ…

Pythagorean Theorem (Chapter 1)

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

4.1

4.2

4.3

4.4

the acute angles of a right triangle are complementary

there can be at most one right or obtuse angle in a triangle

a triangle is equilateral if and only if it is equiangular

each angle of an equilateral triangle measures 60 degrees

4.1

the acute angles of a right triangle are complementary

4.2

there can be at most one right or obtuse angle in a triangle

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…

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…

Corollary 4.1

Corollary 4.2

Corollary 4.3

Corollary 4.4

The acute angles of a right triangle are complementary

There can be at most one right or obtuse angle in a triangle

A triangle is equilateral if and only if it is equiangular

Each angle of an equilateral triangle measures 60 degrees

Corollary 4.1

The acute angles of a right triangle are complementary

Corollary 4.2

There can be at most one right or obtuse angle in a triangle

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 nonlinear points there is exactly one plane…

If two points lie in a plane, then the line containing these 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 nonlinear points there is exactly one plane…

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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…

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…

Ruler Postulate #1

Segment Addition Postulate #2

Protractor Postulate #3

Angle Addition Postulate #4

Ruler Postulate #1... the points on a line can be matched one to…

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

Consider a point A on one side of OB. The rays of the form OA…

if p is in the interior of RST then mRSP+mPSt = mRST

Ruler Postulate #1

Ruler Postulate #1... the points on a line can be matched one to…

Segment Addition Postulate #2

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