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Conclusion

Conditional Statement

Conjecture

Contrapositive

In a conditional statement (if-then statement), the statement…

A statement written in an if then form... A statement of the for…

An educated guess based on known information... pg 78

The statement formed by negating both the hypothesis(educated…

Conclusion

In a conditional statement (if-then statement), the statement…

Conditional Statement

A statement written in an if then form... A statement of the for…

Postulate 2.1

Postulate 2.2

Postulate 2.3

Postulate 2.4

Through any two points, there is exactly one line.

Through any three noncollinear points, there is exactly one p…

A line contains at least two points.

A plane contains at least three noncollinear points.

Postulate 2.1

Through any two points, there is exactly one line.

Postulate 2.2

Through any three noncollinear points, there is exactly one p…

Conclusion

Conditional Statement

Conjecture

Contrapositive

In a conditional statement (if-then statement), the statement…

A statement written in an if then form... A statement of the for…

An educated guess based on known information... pg 78

The statement formed by negating both the hypothesis(educated…

Conclusion

In a conditional statement (if-then statement), the statement…

Conditional Statement

A statement written in an if then form... A statement of the for…

Through any two points, there is exact…

Through any three non-collinear points…

A line contains at least.........?

A plane contains at least.............…

Through any two points, there is exactly one line.

Through any three noncollinear points, there is exactly one p…

A line contains at least two points

A plane contains at least three non-collinear points

Through any two points, there is exact…

Through any two points, there is exactly one line.

Through any three non-collinear points…

Through any three noncollinear points, there is exactly one p…

Conclusion

Conditional Statement

Conjecture

Contrapositive

In a conditional statement, the statement that immediately fo…

A statement of the form "If A, then B." The part following if…

An educated guess.

The statement formed by negating both the hypothesis and conc…

Conclusion

In a conditional statement, the statement that immediately fo…

Conditional Statement

A statement of the form "If A, then B." The part following if…

(Theorem 2.1, Midpoint Theorem) If M i…

(Theorem 2.2, Angle Bisector Theorem)…

(Theorem 2.3) Vertical angles are...

(Theorem 2.4) If 2 lines are perpendic…

1/2 of AB

1/2 m<ABC

congruent

congruent adjacent angles

(Theorem 2.1, Midpoint Theorem) If M i…

1/2 of AB

(Theorem 2.2, Angle Bisector Theorem)…

1/2 m<ABC

Through any two points, there is exact…

Through any three non-collinear points…

A line contains at least.........?

A plane contains at least.............…

Through any two points, there is exactly one line.

Through any three noncollinear points, there is exactly one p…

A line contains at least two points

A plane contains at least three non-collinear points

Through any two points, there is exact…

Through any two points, there is exactly one line.

Through any three non-collinear points…

Through any three noncollinear points, there is exactly one p…

definition of congruent segments

definition of congruent angles

definition of right angles

definition of midpoint

Angle ABC is a right angle... The measure of angle ABC = 90 degr…

definition of congruent segments

definition of congruent angles

If B is between A and C, then

If point D lies in the interior of ㄥAB…

If ㄥABC is a straight angle and D is a…

A line contains at least _____ points;…

AB + BC = AC

mㄥABD + mㄥCBD = mㄥABC

mㄥABD + mㄥCBD = 180॰

2, 3, 4

If B is between A and C, then

AB + BC = AC

If point D lies in the interior of ㄥAB…

mㄥABD + mㄥCBD = mㄥABC

Through any two points, there is exact…

Through any three non-collinear points…

A line contains at least.........?

A plane contains at least.............…

Through any two points, there is exactly one line.

Through any three noncollinear points, there is exactly one p…

A line contains at least two points

A plane contains at least three non-collinear points

Through any two points, there is exact…

Through any two points, there is exactly one line.

Through any three non-collinear points…

Through any three noncollinear points, there is exactly one p…

definition of congruent segments

segment addition postulate

definition of congruent angles

angle addition postulate

two segments that have the same length

if b is between a and c, then ab+bc=ac

angles that have the same measure

if S is in the interior of angle PQR, then the measure of ang…

definition of congruent segments

two segments that have the same length

segment addition postulate

if b is between a and c, then ab+bc=ac

Postulate 2.1 - SAS (Side-Angle-Side)

Postulate 2.2 - ASA (Angle-Side-Angle)

Post 2.3 SSS (Side-Side-Side)

CPCTC (DEFINITION)

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

If two angles and the included side of one triangle are congr…

If three sides of one triangle are congruent to the correspon…

If two triangles are congruent, the six pairs of correspondin…

Postulate 2.1 - SAS (Side-Angle-Side)

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

Postulate 2.2 - ASA (Angle-Side-Angle)

If two angles and the included side of one triangle are congr…

Conclusion

Conditional Statement

Conjecture

Contrapositive

In a conditional statement, the statement that immediately fo…

A statement of the form "If A, then B." The part following if…

An educated guess.

The statement formed by negating both the hypothesis and conc…

Conclusion

In a conditional statement, the statement that immediately fo…

Conditional Statement

A statement of the form "If A, then B." The part following if…

Law of Detachment

Law of Syllogism

Properties of Congruence

Vertical Angles Theorem

If a conditional is true and its hypothesis is true, then its…

If p→q and q→r are true statements, then p→r is a true statem…

Reflexive Property: AB≅AB and ∠A≅∠A. Symmetric Property: If A…

Vertical angles are congruent.

Law of Detachment

If a conditional is true and its hypothesis is true, then its…

Law of Syllogism

If p→q and q→r are true statements, then p→r is a true statem…

Line

Plane

Line Segment

Ray

an infinite set of points that extends in two directions

named using one capitol letter or using four points in the pl…

the line segment AB consists of the points A and B and all po…

the ray AB consists of the initial point A and all points on…

Line

an infinite set of points that extends in two directions

Plane

named using one capitol letter or using four points in the pl…

If-Then/Conditional Statement

Hypothesis

Conclusion

Converse

A statement whose basic format is "If p, the q." There are mu…

"If" part of a conditional statement

"Then" part of a conditional statement

Formed by interchanging the hypothesis and conclusion of a co…

If-Then/Conditional Statement

A statement whose basic format is "If p, the q." There are mu…

Hypothesis

"If" part of a conditional statement

Postulate 2.1

Postulate 2.2

Postulate 2.3

Postulate 2.4

Through an two points, there is exactly one line

Through any three points not on the same line, there is exact…

A line contains at least two points

A plane contains at least three points not on the same line

Postulate 2.1

Through an two points, there is exactly one line

Postulate 2.2

Through any three points not on the same line, there is exact…

2.1 Postulate

2.2 Postulate

2.3 Postulate

2.4 Postulate

through any two points there is one line

through any three noncollinear points there is one plane

one line has at least two points

one plane has at least three noncollinear points

2.1 Postulate

through any two points there is one line

2.2 Postulate

through any three noncollinear points there is one plane

Postulate 2.1... Points and a line

Postulate 2.2... Three points and a plane

Postulate 2.3

Postulate 2.4

Through any two points, there is exactly one line

Through any three points not on the same line, there is exact…

A line contains at least two points

A plane contains at least three points not on the same line

Postulate 2.1... Points and a line

Through any two points, there is exactly one line

Postulate 2.2... Three points and a plane

Through any three points not on the same line, there is exact…

line 1

plane 1

line 2

plane 2

Through any two points, there is exactly one line

Through any three noncollinear points, there is exactly one p…

A line contains at least two points

A plane contains at least three noncollinear points

line 1

Through any two points, there is exactly one line

plane 1

Through any three noncollinear points, there is exactly one p…

Two point postulate

Line point postulate

Line intersection postulate

Three point postulate

Through any two points there is exactly one line

A line contains at least two points

If two lines intersect and then they intersect at exactly one…

Through any three noncollinear points there is exactly one pl…

Two point postulate

Through any two points there is exactly one line

Line point postulate

A line contains at least two points

Segment Addition Postulate

Angle Addition Postulate

Midpoint Theorem

Angle Bisector Theorem

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

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

If M is the midpoint of segment AB, then AM=1/2AB and MB=1/2AB

If BX is the bisector of <ABC, then m<ABX = 1/2m<ABC and m<XB…

Segment Addition Postulate

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

Angle Addition Postulate

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

Inductive Reasoning

Conjecture

Conditional Statement

Hypothesis

reasoning based on patterns you observe

a conclusion you reach using inductive reasoning

an if-then statement

the part following the if

Inductive Reasoning

reasoning based on patterns you observe

Conjecture

a conclusion you reach using inductive reasoning

If B is between A and C, then

If point D lies in the interior of ㄥAB…

If ㄥABC is a straight angle and D is a…

A line contains at least _____ points;…

AB + BC = AC

mㄥABD + mㄥCBD = mㄥABC

mㄥABD + mㄥCBD = 180॰

2, 3, 4

If B is between A and C, then

AB + BC = AC

If point D lies in the interior of ㄥAB…

mㄥABD + mㄥCBD = mㄥABC

Conclusion

Conditional Statement

Conjecture

Contrapositive

In a conditional statement, the statement that immediately fo…

A statement of the form "If A, then B." The part following if…

An educated guess.

The statement formed by negating both the hypothesis and conc…

Conclusion

In a conditional statement, the statement that immediately fo…

Conditional Statement

A statement of the form "If A, then B." The part following if…

definition of congruent segments

segment addition postulate

definition of congruent angles

angle addition postulate

two segments that have the same length

if b is between a and c, then ab+bc=ac

angles that have the same measure

if S is in the interior of angle PQR, then the measure of ang…

definition of congruent segments

two segments that have the same length

segment addition postulate

if b is between a and c, then ab+bc=ac

Conclusion

Conditional Statement

Conjecture

Contrapositive

In a conditional statement (if-then statement), the statement…

A statement written in an if then form... A statement of the for…

An educated guess based on known information... pg 78

The statement formed by negating both the hypothesis(educated…

Conclusion

In a conditional statement (if-then statement), the statement…

Conditional Statement

A statement written in an if then form... A statement of the for…

Definition of Congruence

Segment Addition Postulate

Angle Addition Postulate

Postulate 5

If line segment AB ≅ line segment CD, then AB = CD

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

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

Through any two points, there exists exactly one line.

Definition of Congruence

If line segment AB ≅ line segment CD, then AB = CD

Segment Addition Postulate

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

Conclusion

Conditional Statement

Contrapositive

Converse

In a conditional statement, the statement that immediately fo…

A statement of the form "If p, then q".

If ~ q then ~ p

If q then p

Conclusion

In a conditional statement, the statement that immediately fo…

Conditional Statement

A statement of the form "If p, then q".

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

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

On line AB in a given plane, chose any point O between A and…

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

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

definition of congruent segments

definition of congruent angles

definition of right angles

definition of midpoint

Angle ABC is a right angle... The measure of angle ABC = 90 degr…

definition of congruent segments

definition of congruent angles

definition of congruent segments

definition of congruent angles

definition of right angles

definition of midpoint

Angle ABC is a right angle... The measure of angle ABC = 90 degr…

definition of congruent segments

definition of congruent angles

Segment Addition Postulate

Angle Addition Postulate

Pythagorean Theorem

Linear Pair Theorem

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

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

a2 + b2 = c2

If 2 angles form a linear pair, then they are supplementary

Segment Addition Postulate

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

Angle Addition Postulate

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

If segments, rays or lines meet to for…

If two angles sum to 90° (or form a ri…

If two angles sum to 180° (or form a s…

If two angles are complementary to the…

Then they are perpendicular ... (Definition)

Then they are complementary ... (Definition)

Then they are supplementary... (Definition)

Then they are congruent ... (Theorem)

If segments, rays or lines meet to for…

Then they are perpendicular ... (Definition)

If two angles sum to 90° (or form a ri…

Then they are complementary ... (Definition)

All right angles are congruent

If <1 and <2 are supplementary and <3…

If <4 and <5 are complementary and <6…

vertical angles are congruent

right angles congruence theorem

Congruent Supplements Theorem

Congruent Complements Theorem

vertical angles congruence theorem

All right angles are congruent

right angles congruence theorem

If <1 and <2 are supplementary and <3…

Congruent Supplements Theorem

Inductive Reasoning

Conjecture

Counterexample

Statement

logic used to reach a conclusion or conjecture

A conclusion that is maybe true or false

example that shows that a conjecture is false

a sentence that can be either True or False

Inductive Reasoning

logic used to reach a conclusion or conjecture

Conjecture

A conclusion that is maybe true or false

Reflexive Property Of Equality

Transitive Property Of Equality

Symmetric Property Of Equality

Linear Pair Theorem

A=A.

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

If a = b, then b = a.

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

Reflexive Property Of Equality

A=A.

Transitive Property Of Equality

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

definition of midpoint

biconditional

angle bisector theorem

midpoint theorem

a line/ point divides a segment into two congruent segments

Both the conditional statement and the converse statement are…

If line BX is the bisector of angle ABC, then the measure of…

If M is midpoint of segment AB, then AM= 1/2 AB, and MB= 1/2 AB

definition of midpoint

a line/ point divides a segment into two congruent segments

biconditional

Both the conditional statement and the converse statement are…

Conclusion

Conditional Statement

Conjecture

Contrapositive

In a conditional statement, the statement that immediately fo…

A statement of the form "If A, then B." The part following if…

An educated guess.

The statement formed by negating both the hypothesis and conc…

Conclusion

In a conditional statement, the statement that immediately fo…

Conditional Statement

A statement of the form "If A, then B." The part following if…

conditional statement

converse

inverse

contrapositive

a statement that can be written in the form if p, then q... ex:…

is formed by exchanging the hypothesis and conclusion of the…

formed by negating both the hypothesis and conclusion of the…

formed by negating both the hypothesis and the conclusion of…

conditional statement

a statement that can be written in the form if p, then q... ex:…

converse

is formed by exchanging the hypothesis and conclusion of the…

Conclusion

Conditional Statement

Conjecture

Contrapositive

In a conditional statement, the statement that immediately fo…

A statement of the form "If A, then B." The part following if…

An educated guess.

The statement formed by negating both the hypothesis and conc…

Conclusion

In a conditional statement, the statement that immediately fo…

Conditional Statement

A statement of the form "If A, then B." The part following if…

definition of congruent segments

segment addition postulate

definition of congruent angles

angle addition postulate

two segments that have the same length

if b is between a and c, then ab+bc=ac

angles that have the same measure

if S is in the interior of angle PQR, then the measure of ang…

definition of congruent segments

two segments that have the same length

segment addition postulate

if b is between a and c, then ab+bc=ac

Angle Bisector

Complementary Angles

Congruent Angles

Congruent Segments

A ray that divides an angle into two congruent angles

Two angles whose measures have a sum of 90°

Angles that have the same measure

Two segments that have the same measure

Angle Bisector

A ray that divides an angle into two congruent angles

Complementary Angles

Two angles whose measures have a sum of 90°