Pre Ap/IB Geometry Chapter 2 Test Review
Sample answers
 What is the difference between inductive and deductive reasoning? What do you look for to
tell the difference in a written statement?
Inductive: conclusion based on patterns or examples
Deductive: logical reasoning based on rules or clues
 Do you have to find a general rule to find the next item in a pattern?
Yes! Finding the next without finding rule leads to erroneous answers
 What makes a conjecture false?
One counterexample
 What is a counterexample and when is it used?
A specific example proving a statement false. Used to test the truth value.
 Describe a conditional statement?
Contains if, then (actual or implied); gives a conclusion.
 When can a conditional statement not be true? How do you decide the truth value?
When the hypothesis is true and the conclusion is false. Give counterexample when false.
 What are the two parts of the conditional statement? How do you know which one is which?
Hypothesis and conclusion. If(hypothesis), then (conclusion).
 What is the converse of a conditional statement? Does it always have the same truth value as
its conditional?
If q p (switch hypothesis and conclusion). Does NOT always have the same truth value. If it
does, then the statement can be written as a biconditional.
 When the word then does not appear in a conditional statement, how can you tell which part is
the conclusion?
Explains what will occur based on something else. The “second event” based on the “first
event” (not related to the order in the sentence).
 How can you recognize when to apply the Law of Detachment versus when to apply the Law of
Syllogism?
Law of Detachment – for biconditionals
Law of Syllogism – when more than one conclusion is valid (two separate conditionals)
 When applying the Law of Syllogism, does the order of the conditional statements matter?
Why?
Yes, each conclusion based on the previous.
 What is a biconditional statement?
“if and only if”; both the conditional and its converse are true
 How do you determine the truth value of a biconditional?
Test both conditionals; both must be true. A single counterexample proves false.
 How many conditionals can be written from a biconditional? Do they both have to be true for
the biconditional to be true?
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Two, yes
What type of reasons must be used when writing a proof?
Logical, mathematical. Properties, Postulates, other proven theorems.
How can you remember the difference between the reflexive, symmetric and transitive
properties?
Reflexive – reflect (same); symmetrical – symmetry; transitive – move, across
When filling in missing information in a proof, should you work down the columns or across the
rows?
Across the rows; give reason for each statement
Can a figure help in working a proof?
Yes
How should you mark a figure when starting a proof?
Mark all facts you know based on given information, including any congruent parts, combined
parts with known values, etc.
Does it help to make a plan in writing a proof?
Yes, logically work out your thinking often helps you write statements and reasons.