Chapter 2 HW: pgs. 115-120 #2-58 even
2.
4.
6.
8.
10.
12.
14.
16.
18.
20.
truth value
and
converse
informal proof
Y is the midpoint of XZ
X
Y
Z
-1 > 0 and in a right triangle with right angle C, a2 + b2 = c2.
False
The sum of the measures of two supplementary angles is 180 and -1 > 0.
False
In a right triangle with right angle C, a2 + b2 = c2 or (-1 >0 or the sum of the measures of two
supplementary angles is 180).
True
Converse: If an angle is obtuse, then it measures 120.
False; the measure could be any value other than 120 between 90 and 180.
Inverse: If an angle does not measure 120, then it is not obtuse.
False; the measure could be any value other than 120 between 90 and 180.
Contrapositive: If an angle is not obtuse, then is measure does not equal 120.
True
Converse: If a point lies on they-axis, then its ordered pair has 0 for its x-coordinate;
True
Inverse: If an ordered pair does not have 0 for its x-coordinate, then the point does not lie on the
y-axis.
True
Contrapositive: If a point does not lie on the y-axis, then its ordered pair does not have 0 for its
x-coordinate.
True
True
True
Invalid: vertical angles also have a common vertex.
Invalid
X
Never: The intersection of 2 distinct lines is a point.
Sometimes: Yes, if X, Y, and Z are collinear.
No if
M
Y
Always: One line through QR, one line in a plane
Always: Reflexive Property
22.
24.
26.
28.
30.
32.
34.
36.
38.
Statement
1. M is the midpoint of AB
Q is the midpoint of AM
2. AM = MB
AQ = QM
3. AM + MB = AB
AQ + QM = AM
4. AM + AM = AB
AQ + AQ = AM
5. 2AM = AB
2AQ = AM
6. 2(2AQ) = AB
7. 4AQ = AB
1
8. AQ  AB
4
Reason
1. Given
2. Def. of midpoint
3. SAP
4. Substitution (replacement)
5. Substitution (simplify)
6. Substitution (replacement)
7. Substitution (simplify)
8. Division
40.
Division
42.
Transitive
44.
Statement
x  10
1. x  1 
2
2. 2( x  1)  x  10
3. 2x  2  x 10
4. 2  3x 10
5. 12  3x
6. 4  x
7. x  4
46.
Statement
1. MN = PQ; PQ = RS
2. MN = RS
Reason
1. Given
2.
3.
4.
5.
6.
7.
Multiplication
Distributive
Addition
Addition
Division
Symmetric (POE)
Reason
1. Given
2. Transitive (POE)
48.
Symmetric (POE)
50.
Transitive (POE)
52.
Addition
54. SAP straight up (know to use SAP with working with segments)
Statement
Reason
1. AB = CD
1. Given
2. AB + BC = AC
2. SAP
3. BC + CD = BD
4. CD + BC = AC
3. Substitution
5. BC + CD = AC
4. Commutative Property of Addition
6. AC = BD
5. Substitution or Transitive
or Inverse SAP (add to the given to get to the SAP)
Statement
Reason
1. AB = CD
1. Given
2. BC = BC
2. Reflexive
3. AB + BC = BC + CD
3. Addition
4. AB + BC = AC
4. SAP
BC + CD = BD
5. AC = BD
5. Substitution
or SAP with subtraction
Statement
Reason
1. AB = CD
1. Given
2. AB = AC - BC
2. SAP
3. CD = BD - BC
4. AC - BC = BD - BC
3. Substitution
5. BC = BC
4. Reflexive
6. AC = BD
5. Addition
56.
23o
58.
Statement
1. 1 and 2 form a linear pair.
2. 1 and 2 are supplementary.
3. m1  m2  180
4. m2  2(m1)
5. m1  2(m1)  180
6. 3(m1)  180
3(m1) 180
7.

3
3
8. m1  60
Reason
1. Given
2. Supplement Theorem
3. Def. of suppl. Angles
4. Given
5. Substitution (Replacement)
6. Substitution (Simplify)
7. Division
8. Substitution