Geometry Chapter 2: Reasoning & Proof

Front 1

Hypothesis

Back 1

The "if" part of a conditional statement

Ex: If it is raining, then there are clouds in the sky.

Front 2

Conclusion

Back 2

The "then" part of a conditional statement

Ex: If it is raining, then there are clouds in the sky.

Front 3

Conditional

Back 3

A logical statement that has 2 parts: a hypothesis and conclusion

Ex: If an animal is a bird, then it has feathers.

Front 4

Converse

Back 4

Flipping the conditional: conclusion then hypothesis

Ex: If an animal has feathers, then it is a bird.

Front 5

Inverse

Back 5

Negates(takes the opposite of) the conditional

Ex: If an animal is not a bird, then it does not have feathers.

Front 6

Contrapositive

Back 6

Negates(takes the opposite of) the conditional

Ex: If an animal does not have feathers, then is it not a bird.

Front 7

Biconditional

Back 7

Used when both the conditional and converse are both true

Ex: An animal is warm blooded if and only if it is a mammal.

Front 8

Law of Detachment

Back 8

If the hypothesis of a true conditional statement is true, then the conclusion is true

Ex: Step 1: If you miss curfew, then you are grounded

Step 2: You miss curfew. Therefore, you are grounded.

Front 9

Law of Syllogism

Back 9

If A=B, and B=C, then A=C

Ex: If you miss curfew, then you will get grounded.

If you get grounded, then you will sneak out.

Front 10

Postulate 5

Back 10

Through any 2 points there exists exactly one line.

Front 11

Postulate 6

Back 11

A line contains at least 2 points

Front 12

Postulate 7

Back 12

If 2 lines intersect, then their intersection is exactly one point.

Front 13

Postulate 8

Back 13

Through any 3 noncollinear points there exists exactly one plane

Front 14

Postulate 9

Back 14

A plane contains at least 3 noncollinear points

Front 15

Postulate 10

Back 15

If 2 points lie in a plane, then the line containing them lies in the plane

Front 16

Postulate 11

Back 16

If 2 planes intersect, then their intersection is a line

Front 17

Addition Property

Back 17

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

Ex: 1+2=1+2

Front 18

Subtraction Property

Back 18

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

Ex: 1-0=1-0

Front 19

Multiplication Property

Back 19

If a=b, then ac=bc

Ex: 2(4)=2(4)

Front 20

Division Property

Back 20

If a=b and c is not equal to 0, then a/c=b/c

Ex: 4/2=4/2

Front 21

Substitution Property

Back 21

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

Ex: x=5

x+5=10

5+5=10

Front 22

Distributive Property

Back 22

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

Ex: 2(1+1)=2=2

2+2=4

Front 23

Symmetric Property

Back 23

If a=b then b=a

Ex: x=8, 8=x

Front 24

Reflexive Property

Back 24

a=a

Ex: 12=12

Front 25

Transitive Property

Back 25

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

Ex: y=z

y=2

z=2

Front 26

Theorem 2.1

Back 26

Segment congruence is reflexive, symmetric, and transitive.

Front 27

Theorem 2.2

Back 27

Angle congruence is reflexive, symmetric, and transitive.

Front 28

Theorem 2.3

Back 28

All right angles are congruent

Front 29

Theorem 2.4

Back 29

If 2 angles are supplementary to the same angle, then they are congruent

Ex: If angle 1 and angle 2 are supplementary and angle 3 and angle 2 are supplementary, then angle 1 is congruent to angle 3

Front 30

Theorem 2.5

Back 30

If 2 angles are complementary to the same angle, then they are congruent

Ex: If angle 1 and angle 2 are complementary and angle 3 and angle 2 are complementary, then angle 1 is congruent to angle 3

Front 31

Theorem 2.6

Back 31

Vertical angles are congruent