Geometry Chapter 2 Test: Reasoning and Proof

Thm. 2-1: Vertical Angles Theorem

Vertical angles are congruent. Example: ∠A ≅ ∠B

Reflexive Property of Equality

a = a

Distributive Property of Equality

a(b + c) = ab + ac

supplementary angles

Two angles whose sum is 180 degrees

Good definition

A good definition uses clearly understood terms, is precise and is reversible. Both the conditional and its converse must be true for it to be a good definition. It can be written as a biconditional. Example: Conditional:If points are collinear then they lie on the same line. ~true Converse: If points lie on the same line then they are collinear ~true Biconditional: Points are collinear if and only if they lie on the same line.

biconditional

A single true statement that combines a true conditional and its true converse using the phrase "if and only if"

Thm. 2-4

All right angles are congruent

counterexample

An example that shows that a conjecture is incorrect. Example: Conjecture= If the name of a month starts with the letter J, it is a summer month. Counterexample= January starts with J and it's a winter month.

conditional

An if-then statement.

Transitive Property of Equality

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

Division Property of Equality

If a = b and c ≠ 0, then a/c = b/c

Multiplication Property of Equality

If a = b, then a * c = b * c

Addition Property of Equality

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

Subtraction Property of Equality

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

Symmetric Property of Equality

If a = b, then b = a

Substitution Property of Equality

If a = b, then b can replace a in any expression

Law of Detachment

If a conditional statement is true and its hypothesis is true, then its conclusion is true

Thm. 2-3: Congruent Complements Theorem

If two angles are complementary to the same angle (or of congruent angles, then the two angles are congruent

Thm. 2-5

If two angles are congruent and supplementary, then each is a right angle

Thm. 2-2: Congruent Supplements Theorem

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

Transitive Property of Congruence

If ∠A ≅ ∠B and ∠B ≅ ∠C, then ∠A ≅ ∠C

Symmetric Property of Congruence

If ∠A ≅ ∠B, then ∠B≅ ∠A

complementary angles

Two angles whose sum is 90 degrees

inverse

Negate both the hypothesis and the conclusion of the conditional.

converse

Switch the hypothesis and the conclusion in a conditional.

contrapositive

Switches the hypothesis and the conclusion and negates both.

Law of Syllogism

Takes two conditional statements and forms a conclusion by combining the hypothesis of one statement and the conclusion of another. Example: If a quadrilateral is a square, then it has four right angles. If a quadrilateral has four right angles, then it is a rectangle. Conclusion: If a quadrilateral is a square, then it is a rectangle.

negation

The negation of a statement is the opposite of the statement. . Example: Statement= The sky is blue. Negation = The sky is not blue.

hypothesis

The part of the conditional that comes after the word "if"

conclusion

The part of the conditional that comes after the word "then"

Reflexive Property of Congruence

∠A ≅ ∠A