#### Study sets matching "geometry properties corollaries"

#### Study sets matching "geometry properties corollaries"

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…

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

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

segment addition postulate (2)

angle addition postulate (4)

postulate 5

postulate 6

if B is between A and C, then AB + BC = AC... if AB + BC = AC, th…

if P is in the interior of <RST, then m<RST = <RSP + <PST

through any two points there exists exactly one line

a line contains at least two points

segment addition postulate (2)

if B is between A and C, then AB + BC = AC... if AB + BC = AC, th…

angle addition postulate (4)

if P is in the interior of <RST, then m<RST = <RSP + <PST

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…

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…

Corollary 1

Corollary 2

Corollary 3

Corollary 4

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

Each angle of an equiangular triangle had a measure of 60.

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

The acute angles of a right triangle are complementary

Corollary 1

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

Corollary 2

Each angle of an equiangular triangle had a measure of 60.

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

Ruler Postulate

Segment Addition Postulate

Protractor Postulate

Angle Addition Postulate

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

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

Opposite rays can be paired with 0 and 180 degrees. Rays branc…

If point B lies on the interior of <AOC, then m<AOB + m<BOC =…

Ruler Postulate

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

Segment Addition Postulate

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

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…

Postulate 2.1

Postulate 2.2

Postulate 2.3

Postulate 2.4

Through any two points, there is exactly one line

Through any three noncollinear points, there is exactly one pl…

A line contains at least two points

A plane contains at least three noncollinear points

Postulate 2.1

Through any two points, there is exactly one line

Postulate 2.2

Through any three noncollinear points, there is exactly one pl…

Postulate 1-5: Ruler Postulate

Postulate 1-6: Segment Addition Postula…

Postulate 1-7: Protractor Postulate

Postulate 1-8: Angle Addition Postulate

Every point on a line can be paired with a real number. This m…

If three pints A, B, and C are collinear and B is between A an…

consider ray OB and a point a on one side of ray OB. Every ray…

If point B lies in the interior of ∠AOC then m∠AOB+m∠BOC=m∠AOC.

Postulate 1-5: Ruler Postulate

Every point on a line can be paired with a real number. This m…

Postulate 1-6: Segment Addition Postula…

If three pints A, B, and C are collinear and B is between A an…

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…

Properties of Proportion

Similar polygons

AA Similarity Postulate

SAS Similarity Theorem

1. a/b =c/d is equivalent to:... a.ad=bc b. a/c = b/d c. b/a =…

~ if their vertices can be paired so that: ... 1) Corresponding a…

If 2 angles of one triangle are cingruent ti rqo angles of ano…

if an angle of one triangle is congruent to an angle od anothe…

Properties of Proportion

1. a/b =c/d is equivalent to:... a.ad=bc b. a/c = b/d c. b/a =…

Similar polygons

~ if their vertices can be paired so that: ... 1) Corresponding a…

1

2

3

4

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

Each angle of an equiangular triangle has measure of 60.

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

The acute angles of a right triangle are complementary.

1

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

2

Each angle of an equiangular triangle has measure of 60.

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…

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 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 noncollinear points there is exactly one pla…

Segment Addition Postulate

Angle Addition Postulate

Point, Line, Plane Postulate 1

Point, Line, Plane Postulate 2

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

If P is in the interior of ∠RST, then the measure of ∠RST is e…

Through any two points there exists exactly one line.

A line contains at least two points.

Segment Addition Postulate

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

Angle Addition Postulate

If P is in the interior of ∠RST, then the measure of ∠RST is e…

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

if two angles of a triangle are congrue…

each angle of an equiangular

in a triangle there is at most

acute angles of a right triangle

another triangle the third angles are congruent

triangle has a measure of 60 degrees

one right angle or one obtuse angle

are complementary

if two angles of a triangle are congrue…

another triangle the third angles are congruent

each angle of an equiangular

triangle has a measure of 60 degrees

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…

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…

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…

Theorem 4.1

Theorem 4.2

Theorem 4.3

Corollary 4.1

Angle Sum Theorem- The sum of the measures of the angles of a…

Third Angle Theorem- If two angles of one triangle are congrue…

Exterior Angle Theorem- The measure of an exterior angle of a…

The acute angles of a right triangle are complementary.

Theorem 4.1

Angle Sum Theorem- The sum of the measures of the angles of a…

Theorem 4.2

Third Angle Theorem- If two angles of one triangle are congrue…