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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

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…

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

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 acute

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

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

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

angle less than 90*

Def. of congruent

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

Def. of midpoint

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

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 t…

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

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

Ray that divides an angle into two congruent adjacent angles…

Def. of congruent

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

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…

Vertical angles are congruent.

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

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

Congruent Supplements Theorem

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

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 ar…

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

Angles that have the same measure

Segments that have the same length

Linear pair

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

Angle bisector

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

point

plane

line

collinear points

a location (undefined term)

a flat surface made up of points; has no depth and extends in…

made up of points and has no thickness or width (undefined te…

points on the same line

point

a location (undefined term)

plane

a flat surface made up of points; has no depth and extends in…

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…

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 ... equi…

Lies, Rays, and Segments in Triangles

Perpendicular Bisector Theorem

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

Reflexive Property of Equality (Refl.…

Symmetric Property of Equality (Symm.…

Transitive Property of Equality (Trans…

Substitution Property of Equality (Sub…

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 expres…

Reflexive Property of Equality (Refl.…

a=a

Symmetric Property of Equality (Symm.…

If a=b, the b=a

Triangle Sum Theorem

Exterior Angle Theorem

Corollary to the Triangle Sum Theorem

Properties of Triangle Congruence

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

The measure of an exterior angle of a triangle is equal to th…

The acute angles of a right triangle are complementary.

Triangle congruence is reflexive, symmetric, and transitive.…

Triangle Sum Theorem

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

Exterior Angle Theorem

The measure of an exterior angle of a triangle is equal to th…

Ruler Postulate

Segment Addition Postulate

Protractor Postulate

Angle Addition Postulate

The points on a line can be matched one to one with the real…

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

Consider line OB and a point A on one side of line OB. The ra…

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

Ruler Postulate

The points on a line can be matched one to one with the real…

Segment Addition Postulate

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

Perimeters of Similar Polygons

Areas of Similar Polygons

Angle-Angle (AA) Similarity Theorem

Side-Side-Side (SSS) Similarity Theorem

If two polygons are similar, then the ratio of their perimete…

If two polygons are similar, then the ratio of their areas is…

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

If the corresponding side lengths of... two triangles are propor…

Perimeters of Similar Polygons

If two polygons are similar, then the ratio of their perimete…

Areas of Similar Polygons

If two polygons are similar, then the ratio of their areas is…

they are congruent.... Right Angles Cong…

they are congruent.... Congruent Supplem…

they are congruent.... Congruent Supplem…

they are congruent.... Congruent Complem…

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 Cong…

If two angles are right angles, then

they are congruent.... Congruent Supplem…

If two angles are supplementary to the same angle, then

Triangle Longer Side Theorem

Triangle Larger Angle Theorem

Triangle Inequality Theorem

Pythagorean Theorem

If one side of a triangle is longer than another side, then t…

If one angle of a triangle is larger than another angle, then…

The sum of the lengths of any two sides of a triangle is grea…

In a right triangle, the square of the length of the hypotenu…

Triangle Longer Side Theorem

If one side of a triangle is longer than another side, then t…

Triangle Larger Angle Theorem

If one angle of a triangle is larger than another angle, then…

Classifications of Quadrilaterals

Polygon Interior Angles Theorem

Corollary to the Polygon Interior... Angl…

Polygon Exterior Angles Theorem

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

The sum of the measures of the interior angles of a... quadrilat…

The sum of the measures of the exterior angles of a convex po…

Classifications of Quadrilaterals

Polygon Interior Angles Theorem

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

Tangent Line to a Circle Theorem

External Tangent Congruence Theorem

Arc Addition Postulate

Congruent Circles Theorem

In a plane, a line is tangent to a circle if and ony if the l…

Tangent segments from a common external point are conruent.

The measure of an arc formed by two adjacent arcs is the sum…

Two circles are congruent circles if and only if they have th…

Tangent Line to a Circle Theorem

In a plane, a line is tangent to a circle if and ony if the l…

External Tangent Congruence Theorem

Tangent segments from a common external point are conruent.

they are congruent.... Right Angles Cong…

they are congruent.... Congruent Supplem…

they are congruent.... Congruent Supplem…

they are congruent.... Congruent Complem…

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 Cong…

If two angles are right angles, then

they are congruent.... Congruent Supplem…

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 co…

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 opposit…

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 Cong…

they are congruent.... Congruent Supplem…

they are congruent.... Congruent Supplem…

they are congruent.... Congruent Complem…

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 Cong…

If two angles are right angles, then

they are congruent.... Congruent Supplem…

If two angles are supplementary to the same angle, then

Right Angle Congruence Theorem

Vertical Angles Theorem

Congruent Supplements Theorem

Congruent Complements Theorem

If 2 angles are right angles, then they are congruent

If 2 angles are vertical angles, then they are congruent

If 2 angles are supplementary to the same angle or congruent…

If 2 angles are complementary to the same angle or congruent…

Right Angle Congruence Theorem

If 2 angles are right angles, then they are congruent

Vertical Angles Theorem

If 2 angles are vertical angles, then they are congruent

Midpoint

Collinear

Straight Angles

Acute Angles

It is a midpoint if and only if it divides a segment into two…

3 or more points on the same line

The sides of a straight angle form a line

Acute angles are less than a right angle

Midpoint

It is a midpoint if and only if it divides a segment into two…

Collinear

3 or more points on the same line

Corresponding Angles Converse

Alternate Interior Angles Converse

Alternative Exterior Angles Converse

Consecutive Interior Angles converse

If two lines are cut by a transversal so the corresponding an…

If two lines are cut by a transversal so the alternate interi…

if two lines are cut by a transversal so the alternate exteri…

If two lines are cut by a transversal so the consecutive inte…

Corresponding Angles Converse

If two lines are cut by a transversal so the corresponding an…

Alternate Interior Angles Converse

If two lines are cut by a transversal so the alternate interi…

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 t…

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

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 t…

theorem

postulate

definition

geometry

a statement that can be proved

something we don't need to prove, uses past information to ba…

assigns a term to an object. are always reversible

to take a series of facts to put in a logical way to reach a…

theorem

a statement that can be proved

postulate

something we don't need to prove, uses past information to ba…

segment addition postulate

reflexive property

congruent

midpoint theorem

AB + BC = AC

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

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) (…

Ruler Postulate

Segment Addition Postulate

Protractor Postulate

Angle Addition Postulate

The points on a line can be matched one to one with the real…

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

Consider line OB and a point A on one side of line OB. The ra…

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

Ruler Postulate

The points on a line can be matched one to one with the real…

Segment Addition Postulate

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

Ruler Postulate

Segment Addition Postulate

Protractor Postulate

Angle Addition Postulate

The points on a line can be paired with the real numbers in s…

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…

If B is in the interior of <AOC, then m<AOB + m<BOC = m<AOC.

Ruler Postulate

The points on a line can be paired with the real numbers in s…

Segment Addition Postulate

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

corresponding angles

congruent corresponding angles

SSS Postulate

SAS Postulate

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

If two lines are cut by a transversal and corresponding angle…

If three sides of one triangle are congruent to three sides o…

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

corresponding angles

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

congruent corresponding angles

If two lines are cut by a transversal and corresponding angle…

Segment Addition Postulate

Protractor Postulate

Parallel Lines

Skew Lines

AB + BC = AC

Says that you can measure any angle

two lines that don't intersect and are coplanar

two lines that don't intersect and aren't coplanar

Segment Addition Postulate

AB + BC = AC

Protractor Postulate

Says that you can measure any angle

Parallel Postulate

Perpendicular Postulate

Corresponding Angles Postulate

Alternate Interior Angles Theorem

If there is a line and a point not on the line, then there is…

If there is a line and a point not on the line, then there is…

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

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

Parallel Postulate

If there is a line and a point not on the line, then there is…

Perpendicular Postulate

If there is a line and a point not on the line, then there is…

Perpendicular Bisector Theorem

Corresponding Angles Theorem

Alternate Interior Angles Theorem

Same-Side Interior Angles Postulate

If a point is on the perpendicular bisector of a segment, the…

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

If two parallels are cut by a transversal, then the pair of a…

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

Perpendicular Bisector Theorem

If a point is on the perpendicular bisector of a segment, the…

Corresponding Angles Theorem

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

Corresponding Angles Postulate (3-1)

Alternate Interior Angles Theorem (3-1)

Consecutive Interior Angles Theorem (3…

Alternate Exterior Angles Theorem (3-3)

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

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

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

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

Corresponding Angles Postulate (3-1)

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

Alternate Interior Angles Theorem (3-1)

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

theorem

postulate

definition

geometry

a statement that can be proved

something we don't need to prove, uses past information to ba…

assigns a term to an object. are always reversible

to take a series of facts to put in a logical way to reach a…

theorem

a statement that can be proved

postulate

something we don't need to prove, uses past information to ba…

Ruler Postulate

Segment Addition Postulate

Protractor Postulate

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, the m<AOB a m<BOC =…

Ruler Postulate

1. The points on a line can be paired with the real numbers i…

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 on a line can be matched one to one with the real…

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

The measure of ∠AOB, which can be written as m∠AOB, is equal…

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

Ruler Postulate

The points on a line can be matched one to one with the real…

Segment Addition Postulate

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

Postulate

Theorem

Intersection of 2 lines is exactly...

Intersection of 2 planes is exactly...

Statement accepted without proof

Conjecture (mathematical hypothesis) that has been proved

1 point

1 line

Postulate

Statement accepted without proof

Theorem

Conjecture (mathematical hypothesis) that has been proved

Corresponding Angles Postulate

Alternate Interior Angles Theorem

Alternate Exterior Angles Theorem

Consecutive Interior Angles Theorem.

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

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

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

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

Corresponding Angles Postulate

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

Alternate Interior Angles Theorem

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

Postulate 3-1 Same-side Interior Angle…

Theorem 3-1 Alternate Interior Angles…

Theorem 3-2 Corresponding Angles Theor…

Theorem 3-3 Alternate Exterior Angles…

supplementary... m∠1 + m∠2 = 180

congruent

corresponding

exterior

Postulate 3-1 Same-side Interior Angle…

supplementary... m∠1 + m∠2 = 180

Theorem 3-1 Alternate Interior Angles…

congruent

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 opp…

Complementary angles

two angles whose measures have a sum of 90°

Supplementary angles

two angles who measures have a sum of 180°

Parallel Postulate

Perpendicular Postulate

Corresponding Angles Theorem

Alternate Interior Angles Theorem

If there is a line and a point not on the line, then there is…

If there is a line and a point not on the line, then there is…

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

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

Parallel Postulate

If there is a line and a point not on the line, then there is…

Perpendicular Postulate

If there is a line and a point not on the line, then there is…

Theorem

Theorem 1

Deductive Structure

Postulate

A mathematical statement that can be proved

If two angles are right angles, then they are congruent

A system of thought in which conclusions are justified by mea…

a unproved assumption

Theorem

A mathematical statement that can be proved

Theorem 1

If two angles are right angles, then they are congruent

(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 segme…

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

If figures are congruent, then corresponding segments are con…

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 segme…

(3-9)Definition of bisector:

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

parallel pos.

perpendicular pos.

paragraph proof

transitive property of parallel lines

if there is a line and a point not on that line then there is…

if there is a line and a point not on that line then there is…

a proof written as a paragraph

if two lines are parallel to the same line then they are para…

parallel pos.

if there is a line and a point not on that line then there is…

perpendicular pos.

if there is a line and a point not on that line then there is…

they are congruent.... Right Angles Cong…

they are congruent.... Congruent Supplem…

they are congruent.... Congruent Supplem…

they are congruent.... Congruent Complem…

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 Cong…

If two angles are right angles, then

they are congruent.... Congruent Supplem…

If two angles are supplementary to the same angle, then

Segment addition postulate

Angle addition postulate

Postulate 5

Postulate 6

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

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

A line contains at least two points; a plane contains at leas…

Through any two points there is exactly one line.

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 <AOC, then m<AOB + m<BOC =…

Perpendicular Bisector Theorem

Converse of the Perpendicular Bisector…

Angle Bisector Theorem

Converse of the Angle Bisector Theorem

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

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 ... equi…

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

Perpendicular Bisector Theorem

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

Converse of the Perpendicular Bisector…

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