2.6: Chapter 2 Review
Difficulty Level: At Grade
Created by: CK12
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Keywords
 Inductive Reasoning
 The study of patterns and relationships is a part of mathematics. The conclusions made from looking at patterns are called conjectures. Looking for patterns and making conjectures is a part of inductive reasoning, where a rule or statement is assumed true because specific cases or examples are true.
 Conjecture
 The study of patterns and relationships is a part of mathematics. The conclusions made from looking at patterns are called conjectures.
 Counterexample
 We can disprove a conjecture or theory by coming up with a counterexample. Called proof by contradiction, only one counterexample is needed to disprove a conjecture or theory (no number of examples will prove a conjecture). The counterexample can be a drawing, statement, or number.
 Conditional Statement (IfThen Statement)

Geometry uses conditional statements that can be symbolically written as
p→q (read as “ifp , thenq ”). “If” is the hypothesis, and “then” is the conclusion.
 Hypothesis
 The conditional statement is false when the hypothesis is true and the conclusion is false.
 Conclusion
 The second, or “then,” part of a conditional statement. The conclusion is the result of a hypothesis.
 Converse
 A statement where the hypothesis and conclusion of a conditional statement are switched.
 Inverse
 A statement where the hypothesis and conclusion of a conditional statement are negated.
 Contrapositive
 A statement where the hypothesis and conclusion of a conditional statement are exchanged and negated.
 Biconditional Statement

If
p→ q is true andq→ p is true, it can be written asp→ q . 
If
p is not true, then we cannot concludeq is true. 
If we are given
q , we cannot make a conculsion. We cannot concludep is true.
 Logic
 The study of reasoning.
 Deductive Reasoning
 Uses logic and facts to prove the relationship is always true.
 Law of Detachment

The Law of Detachment states: If
p q is true andp is true, thenq is true. 
If
p is not true, then we cannot concludeq is true 
If we are given
q , we cannot make a conclusion. We cannot concludep is true.
 Law of Contrapositive
 If the conditional statement is true, the converse and inverse may or may not be true. However, the contrapositive of a true statement is always true. The contrapositive is logically equivalent to the original conditional statement.
 Law of Syllogism

The Law of Syllogism states: If
p→ q andq→ r are true, thenp→ r is true.
 Right Angle Theorem
 If two angles are right angles, then the angles are congruent.
 Same Angle Supplements Theorem
 If two angles are supplementary to the same angle (or to congruent angles), then the angles are congruent.
 Same Angle Complements Theorem
 If two angles are complementary to the same angle (or to congruent angles), then the angles are congruent.
 Reflexive Property of Equality

a=a .
 Symmetric Property of Equality

a=b andb=a .
 Transitive Property of Equality

a=b andb=c , thena=c .
 Substitution Property of Equality

If
a=b , thenb can be used in place ofa and vise versa.
 Addition Property of Equality

If
a=b , thena+c=b+c .
 Subtraction Property of Equality

If
a=b , thena−c=b−c .
 Multiplication Property of Equality

If
a=b , thenac=bc .
 Division Property of Equality

If
a=b , thena÷ c=b÷ c .
 Distributive Property

a(b+c)=ab+ac .
 Reflexive Property of Congruence

For Line Segments
AB¯¯¯¯¯¯¯¯≅AB¯¯¯¯¯¯¯¯ For AnglesAB¯¯¯¯¯¯¯¯≅∠ABC≅∠CBA
 Symmetric Property of Congruence

For Line Segments If
AB¯¯¯¯¯¯¯¯≅CD , thenCD¯¯¯¯¯¯¯¯≅AB¯¯¯¯¯¯¯¯ For AnglesCD¯¯¯¯¯¯¯¯≅AB¯¯¯¯¯¯¯¯ If∠ABC≅∠DFF≅∠ABC
 Transitive Property of Congruence

For Line Segments If
AB¯¯¯¯¯¯¯¯≅CD¯¯¯¯¯¯¯¯ and \begin{align*}\overline{CD} \cong \overline{EF}\end{align*}, then \begin{align*}\overline{AB} \cong \overline{EF}\end{align*} For Angles If \begin{align*}\angle ABC \cong \angle DEF\end{align*} and \begin{align*}\angle DEF \cong \angle GHI\end{align*}, then \begin{align*}\angle ABC \cong \angle GHI\end{align*}
Review
Match the definition or description with the correct word.
 \begin{align*}5 = x\end{align*} and \begin{align*}y + 4 = x\end{align*}, then \begin{align*}5 = y +4\end{align*} — A. Law of Contrapositive
 An educated guess — B. Inductive Reasoning
 \begin{align*}6(2a + 1) = 12a +12\end{align*} — C. Inverse
 2, 4, 8, 16, 32,... — D. Transitive Property of Equality
 \begin{align*}\overline{AB} \cong \overline{CD}\end{align*} and \begin{align*}\overline{CD} \cong \overline{AB}\end{align*} — E. Counterexample
 \begin{align*}\sim p \rightarrow \sim q\end{align*} — F. Conjecture
 Conclusions drawn from facts. — G. Deductive Reasoning
 If I study, I will get an “\begin{align*}A\end{align*}” on the test. I did not get an \begin{align*}A\end{align*}. Therefore, I didn’t study. — H. Distributive Property
 \begin{align*}\angle A\end{align*} and \begin{align*}\angle B\end{align*} are right angles, therefore \begin{align*}\angle A \cong \angle B\end{align*}. — I. Symmetric Property of Congruence
 2 disproves the statement: “All prime numbers are odd.” — J. Right Angle Theorem — K. Definition of Right Angles
Texas Instruments Resources
In the CK12 Texas Instruments Geometry FlexBook, there are graphing calculator activities designed to supplement the objectives for some of the lessons in this chapter. See http://www.ck12.org/flexr/chapter/9687.
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angle pairs
biconditional statements
CK.MAT.ENG.SE.1.GeometryBasic.2
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CK.MAT.ENG.SE.2.Geometry.2
conclusion
conditional statements
congruence
conjecture
conjectures
contrapositive
converse
counterexamples
deductive reasoning
hypothesis
ifthen statement
ifthen statements
inductive and deductive reasoning
inductive reasoning
inverse
Law of Contrapositive
Law of Detachment
Law of Syllogism
logic
patterns
proof
proofs
reasoning
Segments
theorems
truth tables
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Date Created:
Feb 22, 2012
Last Modified:
Aug 15, 2016
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