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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

segment addition postulate (SAP)

angle addition postulate (AAP)

addition property of equality

subtraction property of equality

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

Angles can be added together if they are adjacent

Adding a value to each side of an equation... if a=b, then a+c=b+c

subtracting a value from each side of an equation ... if a=b the…

segment addition postulate (SAP)

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

angle addition postulate (AAP)

Angles can be added together if they are adjacent

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 ac=bc

if a=b, then a/c=b/c c is ALMOST equal to

Addition Property of Equality

if a=b, then a+c=b+c

Subtraction Property of Equality

if a=b, then a-c=b-c

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

If two angles have the same measuremen…

If the angles are congruent two angles…

If a point, X, is in the interior of <…

segment addition postulate

definition of congruent angles

definition of congruent angles

angle addition postulate

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

segment addition postulate

If two angles have the same measuremen…

definition of congruent angles

Segment Addition postulate

Angle Addition postulate

Linear Pair postulate

Definition of Congruence

If M is between A and B, then AM+MB=AB.

If C is in the interior of ABD, then m<ABC+m<CBD=m<ABD.

If two angles form a linear paire, then they are supplementary.

If measures are equal, then parts are congruent.

Segment Addition postulate

If M is between A and B, then AM+MB=AB.

Angle Addition postulate

If C is in the interior of ABD, then m<ABC+m<CBD=m<ABD.

Ruler Postulate

Segment Addition Postulate

Protector Postulate

Angle Addition Postulate

AB = distance between endpoints

AB+BC=AC if B is between A and C

Ruler Postulate for Angles

Segment Addition Postulate for Angles

Ruler Postulate

AB = distance between endpoints

Segment Addition Postulate

AB+BC=AC if B is between A and C

Ruler Postulate

Segment Addition Postulate

Postulate

Protractor 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.

A rule accepted without proof

An angle can be measured from 0 to 180

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.

segment addition postulate

Def: Midpoint of a segment

Def: Bisector of a segment

angle addition postulate

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

The point that divides the segment into two congruent segments

A line, segment, ray, or plane that intersects the segment at…

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

segment addition postulate

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

Def: Midpoint of a segment

The point that divides the segment into two congruent segments

segment addition postulate

reflexive property of congruence

symmetric property of congruence

Transitive property of congruence

if A,B, and C are collinear, then point B is between A and C…

segment AB is congruent to segment AB

if segment AB is congruent to segment CD, the segment CD is c…

if segment AB is congruent to segment CD and CD is congruent…

segment addition postulate

if A,B, and C are collinear, then point B is between A and C…

reflexive property of congruence

segment AB is congruent to segment AB

Ruler Postulate

Protractor Postulate

Angle Addition Postulate

Segment Addition Postulate

On a number line, every point can be paired with a number and…

Given line AB and a point O on line AB. Consider rays OA and…

The angle addition postulate states that if B is in the inter…

If a point B lies on a line segment , then . That is, the dis…

Ruler Postulate

On a number line, every point can be paired with a number and…

Protractor Postulate

Given line AB and a point O on line AB. Consider rays OA and…

Slopes of parallel lines

Parallel Postulate

Slopes of Perpendicular Lines

Symmetric Property

If 2 nonvertical lines are parallel then their slopes are equ…

Through a point not on a line, there is ONLY ONE parallel to…

If 2 nonvertical lines are perpendicular, then the product of…

If a=b then b=a

Slopes of parallel lines

If 2 nonvertical lines are parallel then their slopes are equ…

Parallel Postulate

Through a point not on a line, there is ONLY ONE parallel to…

Triangle Angle-Sum Theorem

Exterior angle Theorem

Triangle Angle Sum Corollaries

Definition of Congruent Polygons

The sum of the measures of the angles of a triangle is 180

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

The acute angles of a right triangle are complementary... There…

Two polygons are congruent if and only if their corresponding…

Triangle Angle-Sum Theorem

The sum of the measures of the angles of a triangle is 180

Exterior angle Theorem

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

Postulate or axion

Postulate 2.1

Postulate 2.2

Postulate 2.3

A statement that is accepted as true without proof

Through any two distinct points there exists only 1 line

Though any 2 distinct points there exists exactly 1 plane

A line contains at least 2 points

Postulate or axion

A statement that is accepted as true without proof

Postulate 2.1

Through any two distinct points there exists only 1 line

Segment Addition Postulate (SAP)

VAT

Linear Pair Thm

AAP

AB + BC = AC

Two angles are vertical iff their sides form opposite rays

Two adjacent angles form a linear pair iff their non-common s…

Angle Addition Postulate states that if a point S lies in the…

Segment Addition Postulate (SAP)

AB + BC = AC

VAT

Two angles are vertical iff their sides form opposite rays

Alternate Interior Angles Theorem

Same Side Interior Angles Theorem

Alternate Exterior Angles Theorem

Same Side Exterior Angles Theorem

If 2 parallel lines are intersected by a transversal, then al…

If 2 parallel lines are cut by a transversal, then same side…

If 2 parallel lines are cut by a transversal, the alternate e…

If 2 parallel lines are are cut by a transversal, the same si…

Alternate Interior Angles Theorem

If 2 parallel lines are intersected by a transversal, then al…

Same Side Interior Angles Theorem

If 2 parallel lines are cut by a transversal, then same side…

segment addition postulate (SAP)

angle addition postulate (AAP)

addition property of equality

subtraction property of equality

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

Angles can be added together if they are adjacent

Adding a value to each side of an equation... if a=b, then a+c=b+c

subtracting a value from each side of an equation ... if a=b the…

segment addition postulate (SAP)

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

angle addition postulate (AAP)

Angles can be added together if they are adjacent

Conditional Statement

Converse

Inverse

Contraposistive

A logical statement that has two parts; a hypothesis, and a c…

A conditional statement that switches the places of the hypot…

When the hypothesis and conclusion of a conditional statement…

When the hypothesis and conclusion of a conditional statement…

Conditional Statement

A logical statement that has two parts; a hypothesis, and a c…

Converse

A conditional statement that switches the places of the hypot…

Segment Addition postulate

Angle Addition postulate

Linear Pair postulate

Definition of Congruence

If M is between A and B, then AM+MB=AB.

If C is in the interior of ABD, then m<ABC+m<CBD=m<ABD.

If two angles form a linear paire, then they are supplementary.

If measures are equal, then parts are congruent.

Segment Addition postulate

If M is between A and B, then AM+MB=AB.

Angle Addition postulate

If C is in the interior of ABD, then m<ABC+m<CBD=m<ABD.

Corresponding Angle Postulate

Alternate Interior Angle Postulate

Alternate Exterior Angle Postulate

Same-Side Consecutive Interior Angles…

If 2 // lines are cut by a transversal then the corresponding…

If 2 // lines are cut by a transversal then all alternate int…

If 2 angles are cut by a transversal then all alternate exter…

If 2 parallel lines are cut by a transversal then same side i…

Corresponding Angle Postulate

If 2 // lines are cut by a transversal then the corresponding…

Alternate Interior Angle Postulate

If 2 // lines are cut by a transversal then all alternate int…

adjacent angles

liner pair

vertical angle

addition property of equality

share a common side and vertex

two adjacent angles that have a non common side and forms a l…

two non adjacent angles that are formed by two intersecting l…

if a, b and c are real numbers and a=b the a+c = b+c

adjacent angles

share a common side and vertex

liner pair

two adjacent angles that have a non common side and forms a l…

Postulate 2.1

Postulate 2.2

Postulate 2.3

Postulate 2.4

For every two points there is one line

Brought every three non collinear points there is one plane

For every line there are at least two points

Through every plain there are at least three points

Postulate 2.1

For every two points there is one line

Postulate 2.2

Brought every three non collinear points there is one plane

What is a postulate

Postulate: through any two points

Postulate: through any three no collin…

Postulate: two lines intersect in a

A statement that is accepted as true without proof

There is exactly one line

There is exactly one plane

Point (vertex)

What is a postulate

A statement that is accepted as true without proof

Postulate: through any two points

There is exactly one line

commutative property of addition

commutative property of multiplication

associative property of addition

associative property of multiplication

a + b = b +a

ab = ba

(a + b) + c = a + (b + c)

(ab)c = a(bc)

commutative property of addition

a + b = b +a

commutative property of multiplication

ab = ba

commutative property of addition

commutative property of multiplication

associative property of addition

associative property of multiplication

a + b = b +a

ab = ba

(a + b) + c = a + (b + c)

(ab)c = a(bc)

commutative property of addition

a + b = b +a

commutative property of multiplication

ab = ba

transitive property of equality

reflexive property of equality

the angle addition postulate

supplement postulate

If a = b and b = c, then a = c

a = a

Postulate 13: If D is in the interior of angle BAC, then the…

Postulate 14: If two angles form a linear pair, then they are…

transitive property of equality

If a = b and b = c, then a = c

reflexive property of equality

a = a

commutative property of addition

commutative property of multiplication

associative property of addition

associative property of multiplication

a + b = b +a

ab = ba

(a + b) + c = a + (b + c)

(ab)c = a(bc)

commutative property of addition

a + b = b +a

commutative property of multiplication

ab = ba

commutative property of addition

commutative property of multiplication

associative property of addition

associative property of multiplication

a + b = b +a

ab = ba

(a + b) + c = a + (b + c)

(ab)c = a(bc)

commutative property of addition

a + b = b +a

commutative property of multiplication

ab = ba

Commutative Property of Addition

Commutative Property of Multiplication

Associative Property of Addition

Associative Property of Multiplication

a + b = b +a

ab = ba

(a + b) + c = a + (b + c)

(ab)c = a(bc)

Commutative Property of Addition

a + b = b +a

Commutative Property of Multiplication

ab = ba

commutative property of addition

commutative property of multiplication

associative property of addition

associative property of multiplication

a + b = b +a

ab = ba

(a + b) + c = a + (b + c)

(ab)c = a(bc)

commutative property of addition

a + b = b +a

commutative property of multiplication

ab = ba

Alternate Exterior Angle Theorem

Corresponding Angle Postulate

Alternate Interior Angle Theorem

Same Side (Consecutive) Interior Angle…

If 2 parallel lines are cut by a transversal, then alternate…

If 2 parallel lines are cut by a transversal, then correspond…

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

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

Alternate Exterior Angle Theorem

If 2 parallel lines are cut by a transversal, then alternate…

Corresponding Angle Postulate

If 2 parallel lines are cut by a transversal, then correspond…

def. of ≅ ∠s

def. of ∠ bisector

∠ bisector theorem

transitive property of ≅

use when you change from ≅ ∠s to = measures and vice versa

if BD bisects ∠ABC, then ∠ABD ≅ ∠DBC

if AD bisects ∠ABC, m∠ABD = (1/2)m∠ABC

If ∠1 ≅ ∠2 and ∠2 ≅ ∠3, then ∠1 ≅ ∠3

def. of ≅ ∠s

use when you change from ≅ ∠s to = measures and vice versa

def. of ∠ bisector

if BD bisects ∠ABC, then ∠ABD ≅ ∠DBC

commutative property of addition

commutative property of multiplication

associative property of addition

associative property of multiplication

a + b = b +a

ab = ba

(a + b) + c = a + (b + c)

(ab)c = a(bc)

commutative property of addition

a + b = b +a

commutative property of multiplication

ab = ba

commutative property of addition

commutative property of multiplication

associative property of addition

associative property of multiplication

a + b = b +a

ab = ba

(a + b) + c = a + (b + c)

(ab)c = a(bc)

commutative property of addition

a + b = b +a

commutative property of multiplication

ab = ba

Theorem 4.1

Theorem 4.2

Theorem 4.3

Theorem 4.4

All right angles are congruent

If two angles are adjacent and supplementary, then they form…

Angles that form a linear pair are supplementary

If one angle of a linear pair is right, then the other angle…

Theorem 4.1

All right angles are congruent

Theorem 4.2

If two angles are adjacent and supplementary, then they form…

distributive property

addition property of equality

subtraction property of equality

multiplication property of equality

a(b + c) = ab + ac

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

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

If a = b and c = d, then ac = bd

distributive property

a(b + c) = ab + ac

addition property of equality

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

Postulate 2.1

Postulate 2.2

Postulate 2.3

Postulate 2.4

Through any 2 points there is exactly one line

Through any 3 noncollinear points, there is exactly one plane

A line contains at least 2 points

A plane contains at least 3 noncollinear points

Postulate 2.1

Through any 2 points there is exactly one line

Postulate 2.2

Through any 3 noncollinear points, there is exactly one plane

right angle theorem (1)

theorem 2

theorem 3

postulate 1

If two angles are right angles, then they are congruent

If two angles are right angles, then they are congruent

If a conditional statement is true, then the contrapositive i…

Segment Addition (can be used as Angle Addition) - as we prac…

right angle theorem (1)

If two angles are right angles, then they are congruent

theorem 2

If two angles are right angles, then they are congruent

commutative property of addition

commutative property of multiplication

associative property of addition

associative property of multiplication

a + b = b +a

ab = ba

(a + b) + c = a + (b + c)

(ab)c = a(bc)

commutative property of addition

a + b = b +a

commutative property of multiplication

ab = ba

What the Symbols Mean

Linear Pair Theorem

Congruent Supplements Theorem

Right Angles Congruent Theorem

{=} - means that it is Congruent... * - is the symbol for degrees

If two angles form a linear pair, then they are supplementary

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

All right angles are congruent

What the Symbols Mean

{=} - means that it is Congruent... * - is the symbol for degrees

Linear Pair Theorem

If two angles form a linear pair, then they are supplementary

commutative property of addition

commutative property of multiplication

associative property of addition

associative property of multiplication

a + b = b +a

ab = ba

(a + b) + c = a + (b + c)

(ab)c = a(bc)

commutative property of addition

a + b = b +a

commutative property of multiplication

ab = ba

commutative property of addition

commutative property of multiplication

associative property of addition

associative property of multiplication

a + b = b +a

ab = ba

(a + b) + c = a + (b + c)

(ab)c = a(bc)

commutative property of addition

a + b = b +a

commutative property of multiplication

ab = ba

commutative property of addition

commutative property of multiplication

associative property of addition

associative property of multiplication

a + b = b +a

ab = ba

(a + b) + c = a + (b + c)

(ab)c = a(bc)

commutative property of addition

a + b = b +a

commutative property of multiplication

ab = ba

Addition Property (Equality)

Subtraction Property (Equality)

Multiplication Property (Equality)

Division Property (Equality)

If the same number is added to equal numbers, then the sums a…

If the same number is subtracted from equal numbers, then the…

If the equal numbers are multiplied by the same number, then…

If equal numbers are divided by the same... number, then the quo…

Addition Property (Equality)

If the same number is added to equal numbers, then the sums a…

Subtraction Property (Equality)

If the same number is subtracted from equal numbers, then the…

Additive Property

Definition of an Equilateral Triangle

Definition of Complimentary Angles

Definition of Supplementary Angles

If B is on line AC, then AB+BC=AC

If a figure is an isosceles triangle, then it has at least tw…

If two angles are complimentary, then the sum of their angles…

If two angles are supplementary, then the sum of their angles…

Additive Property

If B is on line AC, then AB+BC=AC

Definition of an Equilateral Triangle

If a figure is an isosceles triangle, then it has at least tw…

commutative property of addition

commutative property of multiplication

associative property of addition

associative property of multiplication

a + b = b +a

ab = ba

(a + b) + c = a + (b + c)

(ab)c = a(bc)

commutative property of addition

a + b = b +a

commutative property of multiplication

ab = ba

commutative property of addition

commutative property of multiplication

associative property of addition

associative property of multiplication

a + b = b +a

ab = ba

(a + b) + c = a + (b + c)

(ab)c = a(bc)

commutative property of addition

a + b = b +a

commutative property of multiplication

ab = ba

Through any two points, there is exact…

Through any three noncollinear points,…

A line contains at least two points (p…

A plane contains at least three non co…

What do two points make up?

What do three points make up?

How many points does a line contain

How many points does a plane contain

Through any two points, there is exact…

What do two points make up?

Through any three noncollinear points,…

What do three points make up?

commutative property of addition

commutative property of multiplication

associative property of addition

associative property of multiplication

a + b = b +a

ab = ba

(a + b) + c = a + (b + c)

(ab)c = a(bc)

commutative property of addition

a + b = b +a

commutative property of multiplication

ab = ba

commutative property of addition

commutative property of multiplication

associative property of addition

associative property of multiplication

a + b = b +a

ab = ba

(a + b) + c = a + (b + c)

(ab)c = a(bc)

commutative property of addition

a + b = b +a

commutative property of multiplication

ab = ba