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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

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

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

Definition of a Congruent Segment

Definition of a Segment Bisector

Definition of a Midpoint

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

Segments that have the same length (Used when you switch from…

a line, segment, ray, or plane that intersects a segment at i…

divides the segment into two congruent segments

Segment Addition Postulate

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

Definition of a Congruent Segment

Segments that have the same length (Used when you switch from…

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

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

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 and C is not equal to 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

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

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

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

Inductive Reasoning

Conjecture

Counterexample

Conditional

is a type of reasoning that reaches conclusions based on a pa…

is a conclusion reached by using inductive reasoning.... ex: As…

an example showing that a statement is false.... ex:... STATEMENT:…

is an "if-then" statement.... ex: If you act politely, then you…

Inductive Reasoning

is a type of reasoning that reaches conclusions based on a pa…

Conjecture

is a conclusion reached by using inductive reasoning.... ex: As…

Side-Side-Side Similarity (SSS ~)

Side-Angle-Side Similarity (SAS ~)

Angle-Angle Similarity (AA ~)

Corresponding Angles In Parallel Lines

Where 3 sides of one triangle are proportional to 3 correspon…

Where 2 sides of one triangle are proportional to 2 correspon…

Where 2 angles of one triangle are congruent to 2 angles of a…

Are Congruent

Side-Side-Side Similarity (SSS ~)

Where 3 sides of one triangle are proportional to 3 correspon…

Side-Angle-Side Similarity (SAS ~)

Where 2 sides of one triangle are proportional to 2 correspon…

Complementary

Vertical angles

Substitution/ transitive

Perpendicular

Two angles that the sum equals 90°

each of the pairs of opposite angles made by two intersecting…

If a is congruent to B and B is congruent to c, then a is con…

Two lines that intersect and form a right angle.

Complementary

Two angles that the sum equals 90°

Vertical angles

each of the pairs of opposite angles made by two intersecting…

Definition of Congruence

Definition of Bisector

Definition of Midpoint

Definition of Supplementary angles

switch between saying the lengths are equal to being congruent

to break into 2 different parts

the middle value creates 2 equal segments

sum of 2 angles that equal 180

Definition of Congruence

switch between saying the lengths are equal to being congruent

Definition of Bisector

to break into 2 different parts

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

Angle addition postulate

Segment addition postulate

Linear Pair Postulate

Vertical Angles Theorem

Measure of an angle equals sum of pairs

Measure of a segment equals sum of its parts

If two angles form a linear pair then they are supplementary

Vertical angles are congruent

Angle addition postulate

Measure of an angle equals sum of pairs

Segment addition postulate

Measure of a segment equals sum of its parts

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 and C is not equal to 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

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

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

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

Triangle Angle Sum Theorem

Perpendicular

CPCTC

SSS

The angles in a triangle add to 180

If 2 lines are perpendicular, then they form right angles.

If 2 triangles are congruent, then corresponding sides and/or…

If 3 sides of one triangle are congruent to 3 corresponding s…

Triangle Angle Sum Theorem

The angles in a triangle add to 180

Perpendicular

If 2 lines are perpendicular, then they form right angles.

Complementary

Vertical angles

Substitution/ transitive

Perpendicular

Two angles that the sum equals 90°

each of the pairs of opposite angles made by two intersecting…

If a is congruent to B and B is congruent to c, then a is con…

Two lines that intersect and form a right angle.

Complementary

Two angles that the sum equals 90°

Vertical angles

each of the pairs of opposite angles made by two intersecting…

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

Linear Pair Theorem

Congruent Supplements Theorem

Vertical Angles theorem

Right angle congruence Theorem

1.<1 and <2 form a linear pair 1.Given... 2.Lines BA and BC form…

1.<1 and <2 are supplementary , 1. Given... <2 and <3 are supple…

1.Diagram at right 1. given... 2.<1+<2 form a linear pair 2. Def…

1.<1&<2 are complementary 1.Given... <2&<3 are complementary 2.D…

Linear Pair Theorem

1.<1 and <2 form a linear pair 1.Given... 2.Lines BA and BC form…

Congruent Supplements Theorem

1.<1 and <2 are supplementary , 1. Given... <2 and <3 are supple…

Segment Addition Postulate

Definition of a Congruent Segment

Definition of a Segment Bisector

Definition of a Midpoint

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

Segments that have the same length (Used when you switch from…

a line, segment, ray, or plane that intersects a segment at i…

divides the segment into two congruent segments

Segment Addition Postulate

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

Definition of a Congruent Segment

Segments that have the same length (Used when you switch from…

If three points A, B, C are collinear…

Segments that have the same length (Us…

a line, segment, ray, or plane that in…

If M is the midpoint of AB, then AM =…

Segment Addition Postulate

Definition of a Congruent Segment

Definition of a Segment Bisector

Midpoint Theorem

If three points A, B, C are collinear…

Segment Addition Postulate

Segments that have the same length (Us…

Definition of a Congruent Segment

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

Definition of congruent segments

Definition of a midpoint

Angle addition postulate

AB+BC=AC

segments that have the same length... if congruent then they are…

The point that divides the segment into two congruent segment…

If P is in the interior of <RST then m<RSP+ m<PST= m<RST

segment addition postulate

AB+BC=AC

Definition of congruent segments

segments that have the same length... if congruent then they are…

Given

Transitive Property

Reflexive Property

Symmetric Property

Information presented at beginning of proof

if a = b ... b = c ... a = c

a = a... segment AB is congruent to segment AB... (like a reflectio…

a =b and b = a... (different but equal or balanced)

Given

Information presented at beginning of proof

Transitive Property

if a = b ... b = c ... a = c

definition of angle bisector

definition of parallel lines

definition of perpendicular lines

definition of perpendicular bisector

a ray that divides and angle into two congruent angles <abx≅cbx

lines that are the same perpendicular distance apart and do n…

lines that form right angles <abc is a right angle

perpendicular bisector of a segment is a line, segment or ray…

definition of angle bisector

a ray that divides and angle into two congruent angles <abx≅cbx

definition of parallel lines

lines that are the same perpendicular distance apart and do n…

Addition Property of Congruence

Distribution Property of Congruence

Subtraction Property of Congruence

Multiplication Property of Congruence

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

a(b+c) is congruence to ab+ac

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

Doubles of of congruent quantities are cogruent

Addition Property of Congruence

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

Distribution Property of Congruence

a(b+c) is congruence to ab+ac

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

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

Reflexive Property of Equality

Transitive Property of Equality

Addition Property of Equality

Subtraction Property of Equality

a = a

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

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

If a = b ... Then a - 3 = b - 3

Reflexive Property of Equality

a = a

Transitive Property of Equality

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

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 ) betwen A and…

If point b lies in the interior of <AOC, then ... m<AOC + 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

Segment Addition Postulate

Definition of Angle Bisector

Definition of Congruence

Definition of Complementary Angles

AB+BC=AC

An angle bisector divides an angle into two equal parts

m∠A= m∠B then ∠A≅∠B

Complementary, then the sum is 90 degrees

Segment Addition Postulate

AB+BC=AC

Definition of Angle Bisector

An angle bisector divides an angle into two equal parts

addition property of equality

subtraction property of equality

multiplication property of equality

division property of equality

adding the same thing to both sides

subtracting the same thing to both sides

multiplying the same thing on both sides

dividing the same thing on both sides

addition property of equality

adding the same thing to both sides

subtraction property of equality

subtracting the same thing to both sides

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 and C is not equal to 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

Right angles

Straight angles

Complements of the same angle

Complements of congruent angles

If two angles are ________ _________, they are congruent.

If two angles are ________ ______, they are congruent.

If two angles are ______ of the same ______, they are congrue…

If two angles are _____ of ______ _______, they are congruent.

Right angles

If two angles are ________ _________, they are congruent.

Straight angles

If two angles are ________ ______, they are congruent.

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

What is the reflexive property?

What do you know about vertical angles?

What does the Mid-Point theorem state?

What is the Angle Bisector theorem?

A quantity is congruent (equal) to itself. (a = a)

Vertical angles are congruent.

The segment joining the midpoints of two sides of a triangle…

This is a theorem that states if a line bisects an angle, the…

What is the reflexive property?

A quantity is congruent (equal) to itself. (a = a)

What do you know about vertical angles?

Vertical angles are congruent.

substitution property

reflexice property

symmetric property

midpoint theorem

if a=b, then either a or b can be used in place of each other

a=a

if a=b, then b=a

if M is the midpoint of line AB then line AM is 1/2 of line A…

substitution property

if a=b, then either a or b can be used in place of each other

reflexice property

a=a

Segment Addition Postulate

Definition of a Congruent Segment

Definition of a Segment Bisector

Definition of a Midpoint

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

Segments that have the same length (Used when you switch from…

a line, segment, ray, or plane that intersects a segment at i…

divides the segment into two congruent segments

Segment Addition Postulate

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

Definition of a Congruent Segment

Segments that have the same length (Used when you switch from…

addition property of equality

subtraction property of equality

multiplication property of equality

division property of equality

adding the same thing to both sides

subtracting the same thing to both sides

multiplying the same thing on both sides

dividing the same thing on both sides

addition property of equality

adding the same thing to both sides

subtraction property of equality

subtracting the same thing to both sides