Unit 2: Reasoning and Proofs

Question 1

The Symbol for a Conditional Statement:

Answer 1

p → q

Question 2

Symbol for a Negation:

Answer 2

~p

Question 3

Symbol for a Converse:

Answer 3

q → p

Question 4

Symbol for an Inverse:

Answer 4

~p → ~q

Question 5

Symbol for a Contrapositive:

Answer 5

~q → ~p

Question 6

Symbol for a Biconditional Statement:

Answer 6

p ↔ q (if and only if)

Question 7

A __________ is an unproven statement that is based on observations.

Answer 7

Conjecture

Question 8

You use _________ _________ when you find a pattern in specific cases and then write a conjecture for the general case.

Answer 8

Inductive Reasoning

Question 9

___________ ________ are those numbers that follow each other. They follow in a sequence or in order.

Answer 9

Consecutive Integers

Question 10

An example that disproves a statement (shows that it is false).

Answer 10

Counterexample

Question 11

_________ _________ uses facts, definitions, accepted properties, and the laws of logic to form a logical argument.

Answer 11

Deductive Reasoning

Question 12

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

Answer 12

Law of Detachment

Question 13

If hypothesis p, then conclusion q.
If hypothesis q, then conclusion r.
If hypothesis p, then conclusion r.

Answer 13

Law of Syllogism

Question 14

Name the postulate: Through any two points, there exists exactly one line.

Answer 14

Two Point Postulate

Question 15

Name the postulate: A line contains at least two points.

Answer 15

Line-Point Postulate

Question 16

Name the postulate: If two lines intersect, then their intersection is exactly one point.

Answer 16

Line Intersection Postulate

Question 17

Name the postulate: Through any three noncollinear points, there exists exactly one plane.

Answer 17

Three Point Postulate

Question 18

Name the postulate: A plane contains at least three noncollinear points.

Answer 18

Plane-Point Postulate

Question 19

Name the postulate: If two points lie in a plane, then the line containing them lies in the plane.

Answer 19

Plane-Line Postulate

Question 20

Name the postulate: If two planes intersect, then their intersection is a line.

Answer 20

Plane Intersection Postulate

Question 21

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

Answer 21

Additional Property of Equality

Question 22

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

Answer 22

Subtraction Property of Equality

Question 23

If a = b, then a × c = b × c, c ≠ 0

Answer 23

Multiplication Property of Equality

Question 24

If a =b, then a/c = b/c, c ≠ 0

Answer 24

Division Property of Equality

Question 25

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

Answer 25

Substitution Property of Equality

Question 26

a = a

Answer 26

Reflective Property of Equality

Question 27

If a = b, then b = a

Answer 27

Symmetric Property of Equality

Question 28

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

Answer 28

Transitive Property of Equality

Question 29

For any segment AB, Segment AB ≅ Segment AB

Answer 29

Reflexive Property of Congruence

Question 30

If Segment AB ≅ Segment CD, then Segment CD ≅ Segment AB

Answer 30

Symmetric Property of Congruence

Question 31

If Segment AB ≅ Segment CD and Segment CD ≅ Segment EF, then Segment AB ≅ EF

Answer 31

Transitive Property of Congruence

Question 32

Segments are congruent if and only if they have the same measure: If Segment AB ≅ Segment CD, then AB = CD
If AB = CD, then Segment AB ≅ Segment CD

Answer 32

Definition of Congruence

Question 33

The midpoint of a segment divides the segment into two congruent parts (equal lengths).
If M is the midpoint of segment AB, then AM = MB

Answer 33

Definition of Midpoint

Question 34

If A, B, and C are colinear points and B is between A and C, then AB + BC = AC
(name the postulate)

Answer 34

Segment Addition Postulate

Question 35

The measure of two angles are equal if and only if the angles are congruent.
m∠A = m∠B ↔ ∠A ≅ ∠B

Answer 35

Definition of Congruence

Question 36

An angle measures 90° if and only if it is a right angle.
m∠A = 90° ↔ ∠A is a right angle

Answer 36

Definition of a Right Angle

Question 37

Two angles are complementary if and only if the sum of their measures is 90°.
Complementary ↔ Sum is 90°

Answer 37

Definition of Complementary Angles

Question 38

Two angles are supplementary if and only if the sum of their measures is 180°.
Supplementary ↔ Sum is 180°

Answer 38

Definition of Supplementary Angles

Question 39

An angle bisector divides an angle into two equal parts.

Answer 39

Definition of an Angle Bisector

Question 40

Perpendicular lines form right angles.

Answer 40

Definition of Perpendicular

Question 41

m∠ABD + m∠DBC = m∠ABC
(name the postulate)

Answer 41

Angle Addition Postulate

Question 42

If two angles are vertical, then they are congruent.
Vertical → Congruent

Answer 42

Vertical Angles Theorem

Question 43

If two angles form a right angle, then they are complementary.
Form a Right Angle → Complementary

Answer 43

Compliment Theorem

Question 44

If two angles form a linear pair, then they are supplementary.
Form A Linear Pair → Supplementary

Answer 44

Linear Pair Theorem (Supplement Theorem)

Question 45

If two angles complementary to the same angle, then they are congruent.
(If ∠A is complementary to ∠B and ∠C is complementary to ∠B, then ∠A ≅ ∠C)

Answer 45

Congruent Compliments Theorem

Question 46

If two angles supplementary to the same angle, then they are congruent.
(If ∠A is supplementary to ∠B and ∠C is supplementary to ∠B, then ∠A ≅ ∠C)

Answer 46

Congruent Supplements Theorem