Download Chapter 2 Review Answer Key:

Chapter 2 Review Answer Key:
1)
inverse: If the sky is not clear, then we cannot see the stars at night.
Converse: If we can see the stars at night, then the sky is clear.
Contrapositive: If we cannot see the stars at night, then the sky is not clear.
2)
inverse: If I don’t go to the beach, then I will not be swimming.
Converse: If I go swimming, then I will go to the beach.
Contrapositive: If I don’t go swimming, then I didn’t go to the beach.
3)
inverse: If a point is not on the line, then it is not on the plane.
Converse: If the point is on the line, then it is on the line.
Contrapositive: If the point is not on the plane, then it is not on the line.
4)
inverse: If we don’t use a calculator, then we are not in math class.
Converse: If we are in math class, then we use a calculator.
Contrapositive: If we are not in math class, then we are not using a calculator.
5)
Converse: If two segments have the same length, then they are congruent.
The converse is true.
Two segments are congruent if and only if they then have the same length.
6)
If we are dismissed early from school, then there is a teacher’s meeting.
The converse is false, since on the Wednesday before Thanksgiving is a half day but
there is no teacher’s meeting.
7)
If points A, B and C form a triangle, then these three points are collinear.
The converse is false, because three collinear points cannot form a triangle.
8)
If the temperature is below freezing, then the water freezes.
9)
The water does not freeze.
10)
If I wear a scarf, then the temperature is below freezing.
11)
If I do not wear a scarf, then the temperature is not below freezing.
12)
13)
14)
15)
16)
17)
Subtraction P.E.
Division P. E.
Transitive P.E.
Symmetric P.E.
Addition P.E.
Addition P.E.
18)
19)
Reflexive Property of Congruence
Angle Addition Postulate
20)
21)
Add three to the previous term.
11, 14
22)
Multiply by -2 to the previous term.
23)
Divide by -2 to the previous term.
24)
a) If the newspaper club meets today, then the garbage is going out.
Valid by the Law of Syllogism
64, -128
1
32
,
1
64
b) Invalid.
c) mA is an acute angle
25)
Valid by Law of Detachment
a)
If the angle is 56 degrees, then it is acute by not 34 degrees.
b)
Two angles that are supplementary could be 40o and 140o
c)
If a number is prime, it could be 7, which is not equal to 13.
26)
1) AB  BC, BC  CD
1) Given
2) AB  CD
3) AB = CD
4) AB = x/2 + 5
CD = 3x - 10
2) Transitive Property of Congruence
5)
x
 5  3x  10
2
6) x + 10 = 6x – 20
7) x + 10 –x = 6x – 20 – x
8) 10 = 5x - 20
9) 10 + 20 = 5x – 20 + 20
10) 30 = 5x
11) 30/5 = 5x/5
12) 6 = x
3) Definition of Congruent Segments
4) Given
5) Substitution P.E.
6) Multiplication P.E.
7) Subtraction P.E.
8) Simplify
9) Addition P.E.
10) Simplify
11) Division P.E.
12) Simplify
27)
Statements
Reasons
1) AD  BC, EC  ED
1) Given
2)
3)
4)
5)
6)
7)
8)
9)
2) Given
3) Definition of Segment Congruence
4) Definition of Segment Congruence
5) Segment Addition Postulate
6) Segment Addition Postulate
7) Transitive P.E.
8) Substitution P.E.
9) Subtraction P.E>
10) Definition of Segment Congruence
AD = BC
EC = ED
AE + ED = AD
BE + EC = BC
AE + ED = BE + EC
AE + EC = BE + EC
AE = BE
10) AE  BE
28)
Statements
1) QP = NM
2) MP = MN + QP
3) MP = PQ + NP
4) NQ = QP + NP
5) MP = NQ
Reasons
1) Given
2) Segment Addition Postulate
3) Substitution P.E.
4) Segment Addition Postulate
5) Transitive P.E.
29)
Statements
1) Given: WY  ZX
Reasons
1) Given
A is the midpoint of WY
A is the midpoint of ZX
2) WY = ZX
3) WA = AY and ZA = AX
4) ZX = ZA + AX
WY = WA + AY
5) ZA +AX WA + AY
6) WA + WA = ZA + ZA
7) 2WA = = 2ZA
8) WA = ZA
9) WA  ZA
2) Definition of Congruent Segments
3) Definition of Midpoint
4) Segment Addition Postulate
5)
6)
7)
8)
9)
Substitution
Substitution
Simplify
Division P.E.
Definition of Congruent Segments