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Geometry - Deductive Reasoning - Chapt 2
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Conditional
- a statement that can be written in if-then 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 non-adjacent angles formed by intersecting lines.
Vertical angles
are congruent.
Complementary angles - two angles whose sum is 90°.
Theorem 2-8
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 2-7
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 2-4
If two lines are perpendicular then they form congruent adjacent angles.
Theorem 2-5 converse to Theorem 2-4
If 2 lines form congruent adjacent angles then lines are
perpendicular.
If <3 and <4 are congruent then a is perpendicular to b
Theorem 2-6
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.
Author
Mamadams
ID
290758
Card Set
Geometry - Deductive Reasoning - Chapt 2
Description
review
Updated
2014-12-06T22:36:33Z
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