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Geometry
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MIDTERM EXAM: Chapter 2 Review
Vocabulary
Conditional Statements
Negation
If-then form
Hypothesis
Conclusion
Converse
Inverse
Contrapositive
Equivalent statement
Perpendicular lines
Line perpendicular to a
plane
Biconditional statements
Logical argument
Two-column proof
Law of Detachment
Law of Syllogism
Theorem
Paragraph proof
Key Concepts & Skills
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Write statements in if-then format; identify the hypothesis and conclusion
Write the converse, inverse, and contrapositive of a conditional statement.
Give a counterexample to disprove a statement.
Rewrite a bi-conditional statement as a conditional and its converse
Identify whether reasoning used is inductive or deductive
Find next items in a pattern
Use the Laws of Detachment and Syllogism to draw a conclusion from given statement(s)
Identify the algebraic property illustrated by a statement.
Solve equations and state a reason for each step.
Write two-column proofs proving statements about segments and angles.
Key Points
Conditional
Inverse
Converse
Contrapositive
if – then
negate conditional
switch conditional’s “if” and “then”
negate converse
pq
~p  ~q
qp
~q  ~p
Inductive reasoning: patterns, observation, experience
Deductive reasoning: fact-based
Law of Detachment
Given p  q
Hypothesis happens
Conclusion occurs
Law of Syllogism
If p  q and q  r, then p  r (similar in logic to transitive property)
MD/CR/1-12/Ch. 2 MT Review
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Geometry
Practice Problems
I. Conditional Statements
Write the statement in if-then form. Determine the hypothesis and conclusion, and write the inverse,
converse, and contrapositive.
The game will start at 4:00 if the other team arrives within five minutes.
II. Biconditional Statements
Write the biconditional statement as a conditional and its converse.
A number is divisible by 10 if and only if it ends in 0.
III. Solve for the variable using the given information.
1)
B)
IV. Proving Statements about Segments and Angles
1)
2)
MD/CR/1-12/Ch. 2 MT Review
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Geometry
3)
IV. Algebraic Properties - Identify the property.
mÐS = 45o , then mÐS + 45o = 90o .
1)
If
2)
If UV = VW, then VW = UV.
3)
If AE = EG and EG = JK, then AE = JK.
4)
If
mÐK = 9o , then 3(mÐK ) = 27o
V. Solve for x
1)
3) Find the measure of the missing angles.
MD/CR/1-12/Ch. 2 MT Review
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4) Find the measure of angles 1 and 2.
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Geometry
VI.
Use the Law of Syllogism or the Law of Detachment to write a valid conclusion. If you
cannot make a valid conclusion, write INVALID.
a) If the newspaper club meets today, then it is Thursday
If today is Thursday, then the garbage going out.
b) If it is summer, then school is closed.
School is closed.
c) If an angle measures less than 90, then it is an acute angle.
mA = 42
d) If the sum of two angles is 180, then they are supplementary
If two angles form a linear pair they are supplementary.
VII. Proofs
For #1-3 Use the following Diagram.
1)
Given: m Ð1 = m Ð2
m Ð3 = m Ð4
Prove: m ÐSRT = m ÐSTR
2)
Given:
RP = TQ
PS = QS
Prove: RS = TS
3)
Given:
m ÐSRT = m ÐSTR
m Ð3 = m Ð4
4)
Given:
Ð3 is supplementary to Ð1
Ð4 is supplementary to Ð2
Prove:
Ð3 @ Ð4
Given:
AC ^ BC
Prove:
Ð3 @ Ð2
5)
Prove: m Ð1 = m Ð2
Ð3 is complementary to Ð1
MD/CR/1-12/Ch. 2 MT Review
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