Geometry Unit 2

Question 1

Conditional Statement

Answer 1

A logical statement that has a hypothesis and

conclusion.

Question 2

Hypothesis

Answer 2

The “if” part of conditional statement.

Question 3

Conclusion

Answer 3

The “then” part of the conditional statement.

Question 4

Converse

Answer 4

Formed by switching the hypothesis and conclusions. “If it is raining then the grass is wet” becomes “If the grass is wet then it is raining.”

Question 5

Inverse

Answer 5

Formed by negating the hypothesis and conclusion. “If it is raining then the grass is wet” becomes “If it is not raining then the grass is not wet”.

Question 6

Contrapositive

Answer 6

Formed by negating the converse. Ex: “If it is raining, the grass is wet”. The contrapositive is “If the grass is not wet, it is not raining.”

Question 7

Biconditional

Answer 7

A statement formed by removing the in then and replacing it with if and only if. Both the original and converse must both be true. Ex: “A triangle has three sides. Anything with three sides is a triangle.” becomes
Something is a triangle if and only if it has three sides.

Question 8

Collinear Points

Answer 8

In the same line.

Question 9

Coplanar

Answer 9

In the same plane.

Question 10

Conjecture

Answer 10

An unproven statement based on observations. Ex: “The next number is 14 because they are counting by 2.”

Question 11

Inductive Reasoning

Answer 11

The process of finding a pattern for specific cases and then writing a conjecture for the general case. “Harold is a grandfather. Harold is bald. Therefore, all grandfathers are bald.” Even though both statements are true, the conclusion can be wrong.

Question 12

Counterexample

Answer 12

A specific case for which the conjecture is false. Ex: Number 2 is even is the counterexample for all prime numbers are odd.

Question 13

Deductive Reasoning

Answer 13

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

Question 14

Law of Logic: Law of Detachment

Answer 14

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

Ex: If Steven gets a raise, then Susan will get a raise.

Question 15

Law of Logic: Law of Syllogism (chain rule)

-not always true

Answer 15

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

Major premise: Plants need to carbon dioxide to live. Minor premise: The oak tree is a plant.
Conclusion: The oak tree needs carbon dioxide to live.

Question 16

Two Point Postulate

Answer 16

Through any two points there exists exactly one line.

Question 17

Line-Point Postulate

Answer 17

A line contains at least two points.

Question 18

Line Intersection Postulate

Answer 18

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

Question 19

Three Point Postulate

Answer 19

Through any three noncollinear points there exists exactly one plane.

Question 20

Plane-Point Postulate

Answer 20

A plane contains at least three noncollinnear points.

Question 21

Plane-Line Postulate

Answer 21

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

Question 22

Plane-Intersection Postulate

Answer 22

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

Question 23

Addition Property

Answer 23

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

Question 24

Subtraction Property

Answer 24

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

Question 25

Multiplication Property

Answer 25

If a = b, then ac = bc

Question 26

Division Property

Answer 26

If a = b, and c doesn't equal 0, then a/c = b/c

Question 27

Substitution Property

Answer 27

If a = b, then a can be replaced with b

Question 28

Distributive Property

Answer 28

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

Question 29

Reflexive Property

Answer 29

a=a AB = AB m

Question 30

Symmetric Property

Answer 30

If a= b, then b = a If AB = CD, then CD = AB If m

Question 31

Transitive Property

Answer 31

If a=b and b=c, then = c If AB = CD and CD = EF, then AB = EF If m

Question 32

Proof

Answer 32

A logical argument that shows a statement is true.

Question 33

Two-column proof

Answer 33

A proof that has numbered statements and corresponding reasons that show an argument in logical order

Question 34

Theorem

Answer 34

A statement that can be proven.

Question 35

Right Angles Congruence Theorem

Answer 35

All right angles are congruent.

Question 36

Congruent Supplements Theorem

Answer 36

If two angles are supplementary to the same angle (or congruent angles), then they are congruent.

Question 37

Congruent Complements Theorem

Answer 37

If two angles are complementary to the same angle (or congruent angles), then they are congruent.

Question 38

Linear Pair Postulate

Answer 38

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

Question 39

Vertical Angle Congruence Theorem

Answer 39

Vertical angles are congruent.