Download Logic and Reasoning Test Review

Name:
Date:
Per:
Geometry 1/2, Mr. Ferraro/Mr. Wong
Logic and Reasoning Test Review
Work on these problems to prepare for the upcoming unit test. If you get stuck, bring this review to
afterschool tutoring: Mon/Thu in Room 210, Library otherwise.
%. ← This may be asked on the test!
1. My current grade is
2. Complete the proof below.
2
1
Given: a k b;
3 = 70o
Prove: m6 7 = 70o
m6
4
a
3
b
5 6
8 7
Statement
1. a k b
Reason
1.
2. m6 3 = m6 7
2.
3. m6 3 = 70o
3.
4. m6 7 = 70o
4.
3. The sequence below is arithmetic. Provide the next two terms.
1, 7, 13, 19,
,
4. Given this arithmetic sequence —
n
f(n)
1
3
2
-1
3
-5
4
-9
5
-13
— answer these questions:
(a) What is the rule for finding the nth element?
(b) What is the 100th element?
1
...
...
n
(a)
...
...
100
(b)
5. Consider the diagram at right.
6
(a) 6 V SZ &
X
are vertical 6 s.
Y
(b) 6 XZU & 6
(c) 6 T SZ &
Z
form a linear pair of 6 s. (2 possible answers)
6
are corresponding 6 s.
V
(d) 6 V SZ &
(e) 6 XZU &
U
6
S
are alternate interior 6 s.
6
T
are alternate exterior 6 s.
R
6. Find the value of r:
110
2(r + 5)
o
o
7. If x = 10, is p k q?
50
r
o
(4x + 20)
p
q
8. Find the values of x, y, & z:
(3z + 20)
o
(x + 30)
(2x + 10)
2y
9. Complete each conjecture:
(a) If two 6 s form a linear pair, then:
(b) If two 6 s are vertical 6 s, then:
2
o
o
o
o
10. For each diagram, write the conjecture it represents. Your answers should be in the form
“If
, then
,” so don’t just write, e.g., Linear Pairs Conjecture.
(a)
(b)
(c)
11. Write the converse of the conjecture from #9b:
Is the converse you wrote true? If not, sketch a counterexample.
12. Write the converse of this statement:
If today is Tuesday, then tomorrow is Wednesday.
Is the converse you wrote true? If not, provide a counterexample to disprove it.
13. Quadrilateral ABCD is a parallelogram. Find the missing
6
measures.
B
C
o
60
A
3
D
14. Write each of the following words under the appropriate kind of logical reasoning:
rules, laws, observations, evidence, conjecture, & proof.
inductive reasoning
deductive reasoning
15. For each situation, indicate which kind of reasoning was used — inductive or deductive — and circle
key words that you used to make up your mind.
(a) Maria draws two parallel lines and cuts them with a transversal. She measures the corresponding
angles and finds that they are congruent. She then draws three more sets of parallel lines cut by
transversals and finds each time that their corresponding angles are congruent too. Afterward,
she makes the statement, “Whenever parallel lines are cut by a transversal, corresponding angles
are congruent.”
(b) Fatima draws two parallel lines and cuts them with a transversal. She measures one of the angles
using a protractor and determines that it is 130o . Using the Corresponding Angles Conjectures,
she reasons that the angle corresponding to the one she measured must also measure 130o .
4