Proofs

Question 1

Addition Property

Answer 1

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

Question 2

Subtraction Property

Answer 2

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

Question 2

Multiplication Property

Answer 2

If a=b, then ac=bc

Question 2

Division Property

Answer 2

If a=b, then a/c = b/c provided c doesn’t equal zero

Question 3

Reflexive Property

Answer 3

a=a (any number is equal to itself)

Question 4

Symmetric Property

Answer 4

if a=b, then b=a

Question 5

Transitive Property

Answer 5

If a=b, then b=a

Question 6

Substitution Property

Answer 6

If a=b, then a may be replaced by b in any expression or equation

Question 7

Distributive Property

Answer 7

a(b+c)= ab+ac

Question 8

Simplify/Combine Like Terms (CLT)

Answer 8

Measure of Angle ABD + Measure of Angle ABD = 2(Measure of Angle ABD)

Question 9

Segment Addition Postulate

Answer 9

If A, B, and C are collinear, then point B is between points A and C if and only if AB+BC=AC

Question 10

Angle Addition Postulate

Answer 10

D is in the interior of Angle ABC if and only if measure of angle ABD + measure of Angle DBC= measure of angle ABC

Question 11

Linear Pair Postulate

Answer 11

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

Question 12

Vertical Angles Theorum

Answer 12

If two angles are vertical angles, then they are Congruent (and have equal measures)

Question 13

Right Angles are Congruent

Answer 13

If angles are right Angles, then they are congruent

Question 14

Definition of Congruence

Answer 14

If AB=CD, then Segment AB is congruent to Segment CD

Question 15

Definition of Perpindicular

Answer 15

Lines that intersect to form a right angle

Question 16

Definition of Angle Bisector

Answer 16

A ray that divides an angle into two congruent angles

Question 17

Definition of a Right Angle

Answer 17

an angle whose measure is 90 degrees

Question 18

Definition of Supplementary Angles

Answer 18

2 angles whose sum is 180 degrees

Question 19

Definition of Complementary Angles

Answer 19

2 angles whose sum is 90 degrees

Question 20

Definition of Segment Bisector

Answer 20

A segment, line, or plane that intersects a segment at its midpoint

Question 21

Definition of Midpoint

Answer 21

The point on a segment that divides a segment into 2 congruent segments (or 2 equal segments)

Question 22

Postulate

Answer 22

Things that we accept without proof

Question 23

Theorum

Answer 23

Things that require proof

Question 24

Hypothesis

Answer 24

If statement

Question 25

Conclusion

Answer 25

Then statement

Question 26

conditional statement

Answer 26

An if-then statement often taken to be true Symbol: p-q Same truth value as contrapositive

Question 27

Converse

Answer 27

A statement is made by exchanging the hypothesis and the conclusion Sympol: q-p Same truth vale as Inverse

Question 28

Inverse

Answer 28

A statement is made by keeping the order of the conditional, but give the negation of the hypothesis and the conclusion Symbol: ~p---~q Same truth value as the inverse

Question 29

Contrapositive

Answer 29

A statement is made by exchanging and negating the hypothesis and the conclusion Symbol: ~q--- ~p Same truth value as the Conditional

Question 30

Biconditional

Answer 30

The conjunction of a conditional statement and its converse. Biconditional statements are written with the phrase, "if and only if", which is abbreviated "iff". If both the conditional and its converse are true, then the biconditional is true

Question 31

Inductive Reasoning

Answer 31

the process of reaching a conclusion based on a pattern, assuming an a served pattern will continue or making an educated guess based on known information

Question 32

Deductive Reasoning

Answer 32

uses general facts, rules, definitions, or properties to reach specific valid conclusions.

Question 33

Conjecture

Answer 33

a concluding statement reached using inductive reasoning (educate guess)

Question 34

Counterexample

Answer 34

One example to show that the conjecture is false. This proves that the whole conjecture is false.