# Study sets matching "postulates geometry theorems"

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The Side-Splitter Theorem

Corollary to the side-splitter theorem

The AA Theorem

Corollary to the AA theorem

If a line parallel to one side of a triangle intersects the ot…

If a line parallel to one side of a triangle intersects the ot…

If two angles of one triangle are equal to two angles of anoth…

Two triangles similar to a third triangle are similar to each…

The Side-Splitter Theorem

If a line parallel to one side of a triangle intersects the ot…

Corollary to the side-splitter theorem

If a line parallel to one side of a triangle intersects the ot…

Segment Addition Postulate

Angle Addition Postulate

Definition of Midpoint

Definition of Angle Bisector

If B is between A and C then the length of AC is equal to the…

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

The point which divides the segment into two congruent segments

A ray that divides an angle into two adjacent angles that are…

Segment Addition Postulate

If B is between A and C then the length of AC is equal to the…

Angle Addition Postulate

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

Through any two points...

If two distinct lines intersect...

If two distinct planes intersect...

Ruler Postulate

... there is exactly one line.

...then they intersect at exactly one point.

...they intersect at exactly one line.

Every point on a line can be paired with a real number, the po…

Through any two points...

... there is exactly one line.

If two distinct lines intersect...

...then they intersect at exactly one point.

Segment Addition Postulate

Angle Addition Postulate

Definition of Midpoint & Bisector

Definition of Angle Bisector

If B is between A and C then the length of AC is equal to the…

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

A bisector bisects a line segment at its midpoint which divide…

A ray that divides an angle into two adjacent angles that are…

Segment Addition Postulate

If B is between A and C then the length of AC is equal to the…

Angle Addition Postulate

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

Law of Detachment

law of syllogism

Postulate 2.1 - Two Point Postulate

Postulate 2.2 - Line-Point Postulate

if the hypothesis of a true conditional statement is true, the…

if 'if hypothesis p, then conclusion q' is true and 'if hypoth…

through any two points, there exists exactly one line

a line contains at least two points

Law of Detachment

if the hypothesis of a true conditional statement is true, the…

law of syllogism

if 'if hypothesis p, then conclusion q' is true and 'if hypoth…

Point

Line

Segment

Ray

A dot represented by a letter.

Two points determine a line. A line is never ending.

Two points determine a segment. A segment has a definite end a…

Two points determine a ray. A ray has one definite end and a n…

Point

A dot represented by a letter.

Line

Two points determine a line. A line is never ending.

Ruler Postulate

Segment Addition Postulate

Protractor Postulate

Angle Addition Postulate

The points on a line can be put into a one-to-one corresponden…

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

Given line AB and point O on line AB, all rays that can be dra…

If S is in the interior of <PQR, then m<PQS + m<SQR = m<PQR

Ruler Postulate

The points on a line can be put into a one-to-one corresponden…

Segment Addition Postulate

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

Ruler Postulate

Segment Addition Postulate

Angle Addition Postulate

2-Point Postulate

The points on a line can be matched one to one w/ the real num…

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

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

Through any 2 points, there exists exactly 1 line.

Ruler Postulate

The points on a line can be matched one to one w/ the real num…

Segment Addition Postulate

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

Postulate 1

Postulate 2

Postulate 3

Postulate 4

Ruler Postulate: The points on a line can be paired with the r…

Segment Addition Postulate: If B is between A and C, then AB +…

Protractor Postulate: On line AB in a given plane, choose any…

Angle Addition Postulate: If point B lies in the interior of <…

Postulate 1

Ruler Postulate: The points on a line can be paired with the r…

Postulate 2

Segment Addition Postulate: If B is between A and C, then AB +…

Postulate

Corresponding Angles Postulate

Properties of a rhombus

Properties of a rectangle

Or axiom, is a statement that is accepted as true without proo…

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

If a quadrilateral is a rhombus, then it is a parallelogram ... I…

If a quadrilateral is a rectangle, then it is a parallelogram…

Postulate

Or axiom, is a statement that is accepted as true without proo…

Corresponding Angles Postulate

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

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…

Angle-Side-Angle Congruence Theorem (AS…

Postulate

Theorem

Angle-Angle-Side Congruence Theorem (AA…

If two angles and a side between them are congruent in two dif…

A rule that we accept to be true.

A rule that has been proven to be true.

If two angles and a side not between them are congruent in two…

Angle-Side-Angle Congruence Theorem (AS…

If two angles and a side between them are congruent in two dif…

Postulate

A rule that we accept to be true.

two point postulate

line point postulate

line intersection postulate

three point postulate

through any two points, there exists exactly one line

a line contains at least two points

if two lines intersect, then their intersection is exactly one…

through any three noncollinear points, there exists exactly on…

two point postulate

through any two points, there exists exactly one line

line point postulate

a line contains at least two points

Segment Addition Postulate

Supplement Theorem

Complement Theorem

Congruent Complements theorem

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

if 2 angles form a linear pair, then they are supplementary an…

If the noncommon sides of 2 adjacent angles form a right angle…

if <1+<2=180 and <2+<3=180, then <1 congruent to <3

Segment Addition Postulate

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

Supplement Theorem

if 2 angles form a linear pair, then they are supplementary an…

Ruler Postulate

Segment Addition Postulate

Protractor Postulate

Angle Addition Postulate

The points on a line can be put into a one-to-one corresponden…

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 is in the interior of <PQR, then m<PQS + m<SQR = m<PQR

Ruler Postulate

The points on a line can be put into a one-to-one corresponden…

Segment Addition Postulate

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

Ruler Postulate

Segment Addition Postulate

Protractor Postulate

Angle Addition Postulate

The points of a line can be put into one-to-one correspondence…

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

Let Ray OA and Ray OB be opposite rays in a plane. Ray OA, Ray…

If point B is in the interior of Angle AOC, then the measureme…

Ruler Postulate

The points of a line can be put into one-to-one correspondence…

Segment Addition Postulate

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

Addition property of equality

Subtraction property of equality

Multiplication property of equality

Division property of equality

If a=b, then a+c=b+c

If a=b, then a-c=b-c

If a=b, then a•c=b•c

If a=b and c≠0, then a/c=b/c

Addition property of equality

If a=b, then a+c=b+c

Subtraction property of equality

If a=b, then a-c=b-c

Postulate 1: Ruler Postulate

Postulate 2: Segment Addition Postulate

Postulate 4: The Angle Addition Postula…

Postulate 5

The points on a line can be paired in a one-to-one corresponde…

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

If point D is in the interior of angle ABC, then the m of angl…

Through any two points there is exactly one line.

Postulate 1: Ruler Postulate

The points on a line can be paired in a one-to-one corresponde…

Postulate 2: Segment Addition Postulate

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

Chapter 9 - Tangents, Arcs & Chords

chord

secant

diameter

...

segment whose endpoints lie on a circle

a line that contains a chord

chord that contains center of circle

Chapter 9 - Tangents, Arcs & Chords

...

chord

segment whose endpoints lie on a circle

Segment addition postulate

Angle addition postulate

Through any two points

Through any three points there is at le…

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

If point B lies in the interior of angle AOC, then measurement…

Through any two points there is exactly one line

Through any three points there is at least one plane, and thro…

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 angle AOC, then measurement…

Undefined Terms

Segment AB

Ray AB

The Line Postulate

Points, Lines, and Planes

Consists of points A and B and all the points in between them

Consists of segment AB and all points C such that B is between…

Through any two points there is exactly one line

Undefined Terms

Points, Lines, and Planes

Segment AB

Consists of points A and B and all the points in between them