# Geometry Chapter 2

### 51 terms by thepunk

#### Study  only

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Reasoning and Proof

### Points

Through any two _______ there exists exactly one line.

### line

A _____ contains at least two points.

### exactly one

If two lines intersect, then their intersection is ______ _______ point.

### three

Through any _______ noncollinear points there exists exactly one plane.

### non collinear

A plane contains at least three ___________ points.

### plane

If two points lie in a plane, then the line containing them lies in the ________.

### planes

If two _________ intersect, then their intersection is a line.

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

### Subtraction Property

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

### Multiplication Property

If a=b, then ac=bc.

### Division Property

If a=b and c≠0, then a/c=b/c.

### Substitution Property

If a=b, then a can be substituted for b in any equation or expression.

### Distributive Property

a(b+c)=ab+ac, where a, b, and c are real numbers.

### Reflexive Property

--Real Numbers--For any real number a, a=a.
--Segment Lengths--For any segment, line segment AB, AB=AB
--Angle Measure-- For any angle <A, m<A=m<A

### Symmetric Property

--Real Numbers-- For any real numbers a and b, if a=b, then b=a
--Segment Length-- For any segments _-AB-_ and _-CD-_, if AB=CD, then CD=AB
--Angle Measure-- For any angles <A and <B, if m<A=m<B, then m<B=m<A

### Transitive Property

--Real Numbers-- For any real numbers a, b, and c,if a=b and b=c, then a=c
--Segment Length-- For any segments _-AB-_, _-CD-_, and _-EF-_, if AB=CD, and CD=EF, then AB=EF.
--Angle Measure-- For any angles <A, <B, and <C, if m<A=m<B and m<B=m<C, then m<A=m<C

### Conjecture

An unproven statement that is based on observations.

EXAMPLE: Conjecture: All prime numbers are odd.
Educated guess

### Inductive Reasoning

The process of arriving at a conclusion based on a set of observations or examples

EXAMPLE: Given the number pattern 1,5,9,13,..., you can use inductive reasoning to determine that the next number in the pattern in 17.

### Counterexample

A specific case that shows a conjecture is false.

EXAMPLE: All prime numbers are odd.
Counterexample: 2, a prime number that is not odd.

### Conditional Statement

A logical statement that has two parts, if/then

### Hypothesis

It's what logically comes first after the "if". The "p" of a conditional statement.

### Conclusion

It is what logically comes second after the "then". The "q" of a conditional statement.

Opposite ( ~ )

If q, then p.

If ~p, then ~q.

If ~q, then ~p.

### Logically Equivalent Statements

Two statements that are both True or both False. They both have the same truth value.

### Perpendicular Lines

Lines that intersect at 90 degrees

### Angle Congruence Postulate

Two angles are congruent if and only if their measures are equal.

### Segment Congruence Postulate

Two segments are congruent if and only if they have the same length.

### Supplement Theorem

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

### Ray

One endpoint and all the points of the line on the one side of the endpoint. EXAMPLE: Ray AB (The endpoint is always listed first.)

### Opposite Rays

Two collinear rays with the same endpoint. EXAMPLE: Ray AB and Ray AC (The endpoints are the same, ray go in opposite directions.)

### Definition of Right Angles

If Angle 1 is a right angle
then m Angle 1= 90 degrees

### Definition of Perpendicular Lines

If Line l is perpendicular to line k,
then m<1=m<2=m<3=m<4=90

### Definition of Supplementary Angles

If m<1+m<2 = 180
then <1 is supp. to <2

### Definition of Complementary Angles

If m<1+m<2 = 90
then, <1 is comp. to <2

### Definition of Congruent Angles

If <1 is congruent to <2
then m<1=m<2

### Definition of Segment Bisector

If AB bisects XY at A
then XA=AY

### Definition of Angle Bisector

If BD bisects <ABC
then m<ABD=m<DBC

### Definition of a Midpoint

If M is the midpoint of AB
then AM=MB

### Two angles supplementary to the same angle or to congruent angles are congruent

If <1 supp. <2 and <2 supp. <3
then <1 is congruent <3

### Two angles complementary to the same angle or to congruent angles are congruent

If <1 comp. <2 and <2 comp. <3
then <1 is congruent <3

### All right angles are congruent

If <1 and <2 are right angles
then <1 is congruent <2

### Vertical Angles are Congruent

If Angle 1 is opposite to angle 2
then <1 is congruent <2

m<ABD+m<DBC= m<ABC

XY+YZ=XZ

### Linear Pair Postulate

If <1 and <2 are adjacent and supplementary
then m<1+m<2=180

### Theorem

A statement that must be proved using undefined terms, definitions, postulates or other proven theorems

### Postulate

A statement that is widely accepted without proof.

### Deductive Reasoning

The process by which a person makes conclusions based on previously known facts, definitions, or rules.

Example: