#### 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 numb…

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 numb…

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 i…

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 i…

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, t…

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, t…

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 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…

if 2 angles of one triangle are congru…

____ 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 an…

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 congru…

the third angles are congruent

____ the third angles are congeuent

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

Corollary 1

Corollary 2

Corollary 3

Corollary 4

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

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 an…

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 s…

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

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

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 s…

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…

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

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 p…

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 p…

Postulate 1-5: Ruler Postulate

Postulate 1-6: Segment Addition Postul…

Postulate 1-7: Protractor Postulate

Postulate 1-8: Angle Addition Postulate

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

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

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

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…

Postulate 1-6: Segment Addition Postul…

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

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 poi…

If two planes intersect then they intersect at exactly one li…

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 poi…

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…

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

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

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…

1

2

3

4

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

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…

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 Bis…

Theorem 5.6 (Incenter Theorem)

The perpendicular bisectors of a triangle intersect at a poin…

If a point is on the bisectors of an angle, then it is equidi…

If a point in the interior of an angle is equidistant from th…

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 poin…

Theorem 5.4 (Angle Bisector Theorem)

If a point is on the bisectors of an angle, then it is equidi…

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 pl…

if two points lie in a plane, then the line containing these…

if two lines intersect, then they intersect in exactly one po…

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 pl…

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,…

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

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,…

Angle Addition Postulate

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

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 pair…

If two lines are perpendicular to the same line, then the lin…

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 pair…

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 congru…

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 congru…

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 exact…

...

...

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 exact…

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,…

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

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 tr…

If two sides and the included angle of one triangle are congr…

If two sides and the included side of one triangle are congru…

If two angles and a non included side of one triangle are con…

Side-Side-Side (SSS)

If three sides of one triangle are congruent to the second tr…

Side-Angle-Side (SAS)

If two sides and the included angle of one triangle are congr…

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 congru…

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 congru…