Download PRACTICE Test Chapter 2 Logic and Proofs Start on in class and

PRACTICE Test Chapter 2
Logic and Proofs Start on in class and finish for HW Use notes
Name_________________________
Date___________________________
I. Determine if each conjecture is true or false. Explain your answer and give a counterexample
for a false conjecture.
1. Given: x is an integer
2. Given: <1 and <2 are complementary
Conjecture:  x  0
Conjecture: m 1  m 2
II. Write each conditional statement in IF-Then form. Identify the hypothesis and conclusion.
Then write the converse, inverse, and contrapositive of each conditional statement. Then
determine if each statement is true or false and give counterexample for false statements
5. Two parallel planes do not intersect.
Conditional:
Converse:
Inverse:
Contrapositive:
III. Determine if a valid conclusion can be reached from the two true statements. If it can,
state it and the law of logic that is used. If a valid conclusion does not follow, write no
conclusion or invalid. Use Law of Detachment or Law of Syllogism
7. 1) If two angles are supplementary, then the sum of the two angles is 180.
2) < A and < B are supplementary
3)
8. 1) If fossil fuels are burned, then acid rain is produced.
2) If acid rain is produce, then wildlife suffers.
3)
9.
1) All integers are real numbers
2) 17 is a real number
3)
IV. 10. Write a two – column proof. State the given and prove statements.
3
4
Prove that if (16 x  32)  5 x  (14 x  28)  11, then x  29
4
7
Given:
Prove:
Statement
Reason
VI. Name the property of equality that justices each statement. Identify if addition or
multiplication.
11.
12.
13.
14.
15.
16. If
17.
If m<A = m<B, then m<B = m<A.
If AB = 7 and 7 = CD, then AB = CD.
mZ  mZ
If x + 9 = 12, then x = 3.
3( 4x -5) = 12x -15
EF = GH and GH = JK, then EF = JK.
If 1y 17, then y 17.
V. Find the measure of each numbered angle. Show all work and the equation.
18. m<1 = x 2  6 x
m<2 = 8 x  40
1
19. m< 1 = x 2  5 x
m<2 = 26x
20. m<1= 4x - 5
m<2 = 3x +7
m<3 = 2x + 16
2
1
2
1
2
3
Use the given information to write and equation. Solve the equation to find the measures of
the two angles.
1
1
21. < R and < S form a linear pair. If the m< R = x  15 and m< S = 2 x  15
2
2
Find value of x and m< R and m<S.
22. Given < 1 and < 2 are vertical angles. m 1 = 700 and m 2  x 2  9 x .
Find x and < 1and < 2
23. The measure of one of two complementary angles is six less than twice the measure of
the other angle.
24. Suppose “ p “ stands for I like DSF, and “ q” stands for I like Geometry.
Express in words each of the following statements ( page 576 in your book)
A. ~ q ~ p B. q  p
C. p  q
D. ~ p  ~ q