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Conditional  a statement that can be written in ifthen form
a. hypothesis  the given information
b. conclusion  what you are trying to prove
symbolic: p ⇒ q

Negation  opposite of the original statement. it is or it isn't
symbolic: ~ p

Counterexample  an example that proves that a statement is false.

Converse  statement made by exchanging the hypothesis and conclusion.
Inverse  statement made by negating both the hypothesis and conclusion
Contrapositive  statement made by negating both the hypothesis and conclusion of the converse.

Equivalent statements  same truth value
Rules:
contrapositive and counterexample always the same
inverse and converse always the same.

Logic rule: p ⇒ q, if given q ⇒ p
All cows eat grass.
Elsey is a cow then she sat grass.

biconditional  combining a true conditional with its true converse using if and only if.



State the property that justifies each statement.
1. If m <1 = m <2 , then m <2 = m <1.
2. If m<1 = 90 and m <2 = m<1, then m <2 = 90.
3. If AB = RS and RS = WY, then AB = WY.
4. If AB = CD, then 1/2AB = 1/2CD.
5. If m <1 + m <2 = 110 and m <2 = m <3, then m <1 + m <3 = 110.
6. RS = RS
7. If AB = RS and TU = WY, then AB + TU = RS + WY.





Vertical angles  two nonadjacent angles formed by intersecting lines.

Vertical angles are congruent.

Complementary angles  two angles whose sum is 90°.

Theorem 28
Congruent Complements Theorem
If two angles are complements of the same < or congruent < then the angles are congruent.

supplementary angles  two angles whose sum is 180°.

Theorem 27
Congruent Supplements Theorem
If two angles are supplements of the same < or congruent < then the angles are congruent.

Linear pair
* two adjacent angles whose non common sides are line
* always supplementary (180°)

Perpendicular lines: two lines that intersect to form a right angle. (90°)

Theorem 24
If two lines are perpendicular then they form congruent adjacent angles.

Theorem 25 converse to Theorem 24
If 2 lines form congruent adjacent angles then lines are perpendicular.
If <3 and <4 are congruent then a is perpendicular to b

Theorem 26
If the exterior sides of two adjacent acute angles are perpendicular then the angles are complementary.

Inductive reasoning  basing a conclusion on observations only. This doesn't have to be true.
Deductive reasoning  basing a conclusion on a fact. If the hypothesis is true, so is the conclusion.

Law of Detachment: if p → q is true and p is true then q is true.

Law of Syllogism: if p → q and q → r are true, then p → r is true.

