# Study sets matching "geometry postulates math theorems"

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Segment Addition postulate

Alternate Interior Angles Theorem

Alternate Exterior Angles Theorem

Same-Side Interior Angles Theorem

AB+BC=AC

If two parallel lines are cut by a transversal then the pair o…

If two parallel lines are cut by a transversal then the pair o…

If two parallel lines are cut by a transversal then the pair o…

Segment Addition postulate

AB+BC=AC

Alternate Interior Angles Theorem

If two parallel lines are cut by a transversal then the pair o…

Transitive Property

symmetric property

reflexive property

substitution property

if a=b and b=c then a=c

if a=b then b=a

for any real number a, a=a

if a=b then a can be substituted for binary equation/expression

Transitive Property

if a=b and b=c then a=c

symmetric property

if a=b then b=a

converse of the Alternate Interior Angl…

converse of the same-side interior angl…

converse of the alternate exterior angl…

converse of the corresponding angles th…

If two lines and a transversal form alternate interior angles…

If two lines and a transversal form same-side interior angles…

if two lines and a transversal form alternate exterior angles…

if two lines and a transversal form corresponding angles that…

converse of the Alternate Interior Angl…

If two lines and a transversal form alternate interior angles…

converse of the same-side interior angl…

If two lines and a transversal form same-side interior angles…

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.

Collinear Points

Noncollinear Points

Coplanar Points

Noncoplanar

Points that are all in one line

Points that are not in one line

Points that are in one plane

Points that are in multiple planes

Collinear Points

Points that are all in one line

Noncollinear Points

Points that are not in one line

Def. of congruent

Def. of midpoint

Segment bisector

Def. of angle bisector

When two angles or lines are equal size. ... Ex. If line AD=BC th…

Divides a segment into two congruent segments... Ex. If f is the…

Point, line, segment, Ray, or plane, that divides a segment in…

Ray that divides an angle into two congruent adjacent angles... E…

Def. of congruent

When two angles or lines are equal size. ... Ex. If line AD=BC th…

Def. of midpoint

Divides a segment into two congruent segments... Ex. If f is the…

Congruent Supplements Theorem

Vertical Angles Theorem

Alternate interior angles theorem

Alternate exterior angles theorem

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

Vertical angles are congruent.

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

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

Congruent Supplements Theorem

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

Vertical Angles Theorem

Vertical angles are congruent.

Linear pair

Angle bisector

Congruent angles

Congruent segments

Two adjacent angles that form online who's noncommon sides are…

A line, ray, or segment that divides an angle into two adjacen…

Angles that have the same measure

Segments that have the same length

Linear pair

Two adjacent angles that form online who's noncommon sides are…

Angle bisector

A line, ray, or segment that divides an angle into two adjacen…

Reflexive Property of Equality (Refl. P…

Symmetric Property of Equality (Symm. P…

Transitive Property of Equality (Trans.…

Substitution Property of Equality (Subs…

a=a

If a=b, the b=a

If a=b and b=c, the a=c

If a=b, then a may be replaced by b in any equation or express…

Reflexive Property of Equality (Refl. P…

a=a

Symmetric Property of Equality (Symm. P…

If a=b, the b=a

Complementary angles

Supplementary angles

Theorem

Vertical Angles

two angles whose measures have a sum of 90°

two angles who measures have a sum of 180°

a statement that can be proven

two angles formed by intersecting lines and facing in the oppo…

Complementary angles

two angles whose measures have a sum of 90°

Supplementary angles

two angles who measures have a sum of 180°

Exterior angle inequality thm

Addition prop of inequality

Subtraction prop of inequality

Multiplication prop of inequality

the meas. of an ext. angle of a triangle is > than either remo…

If a > b and c > or = to d, then a + c > b + d

If a > b and c = d, or if c = d and a > b, then a - c > b - d,…

If a > b and c > 0, then ca > cb... If a > b and c < 0, then ca <…

Exterior angle inequality thm

the meas. of an ext. angle of a triangle is > than either remo…

Addition prop of inequality

If a > b and c > or = to d, then a + c > b + d

they are congruent.... Right Angles Congr…

they are congruent.... Congruent Suppleme…

they are congruent.... Congruent Suppleme…

they are congruent.... Congruent Compleme…

If two angles are right angles, then

If two angles are supplementary to the same angle, then

If two angles are supplementary to congruent angles, then

If two angles are complementary to the same angle, then

they are congruent.... Right Angles Congr…

If two angles are right angles, then

they are congruent.... Congruent Suppleme…

If two angles are supplementary to the same angle, then

Classifications of Quadrilaterals

Polygon Interior Angles Theorem

Corollary to the Polygon Interior... Angle…

Polygon Exterior Angles 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…

Classifications of Quadrilaterals

Polygon Interior Angles Theorem

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

they are congruent.... Right Angles Congr…

they are congruent.... Congruent Suppleme…

they are congruent.... Congruent Suppleme…

they are congruent.... Congruent Compleme…

If two angles are right angles, then

If two angles are supplementary to the same angle, then

If two angles are supplementary to congruent angles, then

If two angles are complementary to the same angle, then

they are congruent.... Right Angles Congr…

If two angles are right angles, then

they are congruent.... Congruent Suppleme…

If two angles are supplementary to the same angle, then

Linear Pairs are Supplementary.

Perpendicular Lines form right angles.

All right angles are congruent.

Supplements of congruent angles are con…

Right

Supplementary (Working with total of 4 angles)

Linear Pairs are Supplementary.

Perpendicular Lines form right angles.

Complementary Angles

Supplementary Angles

Adjacent Angles

Linear Pair of Angles

2 angles whose sum is always 90 degrees

2 angles whose sum is always 180 degrees

A pair of angles that share a common side, and have no common…

A pair of adjacent angles whose non-common sides form opposite…

Complementary Angles

2 angles whose sum is always 90 degrees

Supplementary Angles

2 angles whose sum is always 180 degrees

they are congruent.... Right Angles Congr…

they are congruent.... Congruent Suppleme…

they are congruent.... Congruent Suppleme…

they are congruent.... Congruent Compleme…

If two angles are right angles, then

If two angles are supplementary to the same angle, then

If two angles are supplementary to congruent angles, then

If two angles are complementary to the same angle, then

they are congruent.... Right Angles Congr…

If two angles are right angles, then

they are congruent.... Congruent Suppleme…

If two angles are supplementary to the same angle, then

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, c not equal to "zero", 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

Reflexive Property of Equality

Symmetric Property of Equality

Transitive Property of Equality

Addition Property of Equality

a = a

If a = b... Then b = a

If a = b, and b = c ... Then a = c

If a = b ... Then a + 3 = b + 3

Reflexive Property of Equality

a = a

Symmetric Property of Equality

If a = b... Then b = a

Lies, Rays, and Segments in Triangles

Perpendicular Bisector Theorem

Converse of the Perpendicular Bisector…

Angle Bisector Theorem

In a plane, if a point lies on the perpendicular bisector of a…

In a plane, if a point is equidistant from the endpoints of a…

If a point lies on the bisector of an angle, then it is ... equid…

Lies, Rays, and Segments in Triangles

Perpendicular Bisector Theorem

In a plane, if a point lies on the perpendicular bisector of a…

(2-4)Definition of midpoint:

(3-9)Definition of bisector:

(5-2)CPCF Theorem (segment):

(2-4)Definition of a circle:

If a point is the midpoint of a segment, it divides the segmen…

If a figure is the the bisector of a segment, it divides the s…

If figures are congruent, then corresponding segments are cong…

If a figure is a circle, then its radii are congruent. (2-4)

(2-4)Definition of midpoint:

If a point is the midpoint of a segment, it divides the segmen…

(3-9)Definition of bisector:

If a figure is the the bisector of a segment, it divides the s…

Chapter 1

Postulate 5- A line contains

Postulate 5 (cont.) A plane contains

Postulate 5 (cont) Space contains

FUN

at least two points

at least three points not all in one line

at least four points not all in one plane.

Chapter 1

FUN

Postulate 5- A line contains

at least two points

Triangle Sum Theorem

Exterior Angle Theorem

Exterior Angle Inequality Theorem

Triangle Inequality Theorem

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…

the measure of an exterior angle of a triangle is greater than…

the sum of the lengths of any 2 sides of a triangle is greater…

Triangle Sum Theorem

the sum of the measures of the interior angles of a triangle i…

Exterior Angle Theorem

the measure of an exterior angle of a triangle is equal to the…

segment addition postulate

reflexive property

congruent

midpoint theorem

AB + BC = AC

any segment or angle is congruent/equal to itself (AB = AB) (m…

have equal measure

If AB + BC = AC and AB=BC

segment addition postulate

AB + BC = AC

reflexive property

any segment or angle is congruent/equal to itself (AB = AB) (m…