Reasoning and Proof Unit Test

Definition of Supplementary Angles

Two angles with measures that have a sum of 180.

Definition of Complementary Angles

Two angles with measures that have a sum of 90.

Definition of a Vertical Angle

Two non-adjacent angles formed by two intersecting lines.

Vertical Angles Theorem

Vertical angles are congruent.

Conditional Statements

Logical statements that have 2 parts and are only true under certain conditions. (ex: If a horse is a racehorse, then it is at least 2 years old.)

Definition of Linear Pair

A pair of adjacent supplementary angles.

Definition of Angle Bisector

A ray that divides an angle into 2 congruent angles.

Conclusion

A summary based on evidence or facts. (ex: It is at least 2 years old.)

Definition of a Right Angle

An angle that measures 90 degrees.

Hypothesis

An educated guess. (ex: A horse is a racehorse.)

Counter Example

An example that shows a conjecture is false. (conjecture: If a horse is at least 2 years old, then it is a racehorse. counter example: The horse could be a showjumper.)

Conjecture

An opinion or conclusion formed on the basis of incomplete information.

Converse

Exchange the hypothesis and the conclusion. (ex: If a horse is at least 2 years old, then it is a racehorse.)

Definition of Congruence

Having the same measure.

Segment Addition Postulate

If B is between A and C, then AB+BC=AC (part+part=whole)

Midpoint Theorem

If M is the midpoint of AB, then AM is congruent to MB

Angle Addition Postulate

If point B lies in the interior of <AOC then m<AOB+m<BOC=m<AOC (part+part=whole)

Complement Theorem

If the non-common sides of two adjacent angles form a right angle, then the angles are complementary angles.

Right Angle Theorem

If two angles are both supplementary and congruent, then they are right angles.

Congruent Complements Theorem

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

Congruent Supplements Theorem

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

Supplement Theorem

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

Reflexive Property of Equality

If x, then x=x

Transitive Property of Equality

If x=y and y=z, then x=z

Substitution Property of Equality

If x=y, then x can be substituted in for y in any equation, and y can be substituted for x in any equation.

Addition Property of Equality

If x=y, then x+z=y+z

Subtraction Property of Equality

If x=y, then x-z=y-z

Division Property of Equality

If x=y, then x/z=y/z

Multiplication Property of Equality

If x=y, then xz=yz

Symmetric Property of Equality

If x=y, then y=x

Definition of Perpendicular

Lines that form right angles.

Contrapositive

Negates hypothesis and conclusion, then switches them. (ex: If a horse is not a racehorse, then it is not 2 years old.)

Inverse

Negates hypothesis and conclusion. (ex: If the horse is not a racehorse, then it is not a Thoroughbred.)

Inductive Reasoning

Reasoning based on observed patterns.

Logically Equivalent

Statements that have the same truth values. The conditional statement and contrapositive have the same truth value while the inverse and converse have the same truth value.

If-then Form

The "if" part is the hypothesis and comes first, and the "then" part is the conclusion. (ex: If the a horse is a racehorse, then it is at least 2 years old.)

Negation

The opposite of the original statement. (Ex: The horse is a Thoroughbred. Negation: The horse is NOT a Thoroughbred.)

Definition of Midpoint

The point on a segment that is exactly halfway between the endpoints.

Deductive Reasoning

The process of applying a general statement to specific facts or situations.

Distributive Property

x(y+z)=xy+xz