Transcript Ac2.2cWrittenEx - wideworldofgeometry

“Indubitably.”
“The proof is in the pudding.”
Le pompt de pompt le solve de crime!"
Deductive Reasoning
Je solve le crime. Pompt de pompt pompt."
2.2cWritten Ex.
Justify each step.
+5
1
+5
4x – 5 = - 2
Given
4x = 3
___
__
4
4
Addition Prop. Of Equality
x
Division Prop. Of Eq.
3
4
2
2
3a 26

2
5
3a 
3
a
12
Given
Multiplication Prop. Of Equality
35
4
5
Division Prop. Of Eq.
The question you
need to ask is…
What did I do to
get to the next
step?
The question you need to ask is…
What did I do to get to the next step?
Justify each step.
3
3 z7
3
  11
Given
3
Z + 7 = - 33
-7
-7
Subtr. Prop. Of Equality
z = - 40
4
Multiplication Prop. Of Equality
15y + 7 = 12 – 20y
+20y
Given
+20y
35y + 7 = 12
-7
-7
35y
5
___ =___
35
Addition Prop. Of Equality
Subtr. Prop. Of Equality
35
y
1
7
Division Prop. Of Eq.
5
3 2
3(
b  8  2b
)
Justify each step.
Given
3
The question you need to ask is…
What did I do to get to the next step?
2 b  3  8  2 b  Multiplication Prop. Of Equality
2 b  24  6 b
6b
+6b
___
8 b  ___
24
8
8
b=3
6
x2
2x  8
5
5(x – 2) = 2x + 8
5x - 10 = 2x + 8
3x - 10 = 8
3x = 18
x= 6
Distributive Prop.
Addition Prop. Of Equality
Division Prop. Of Eq.
Given
Multiplication Prop. Of Equality
Distributive Prop.
Subtr. Prop. Of Equality
Addition Prop. Of Equality
Division Prop. Of Eq.
7 Given:  A O D as show n
A
B
?
Prove:
m  AOD  m  1  m  2  m  3
1
C
2
3
Label diagram to help visualize.
Statements
m  AOD  m  AOC  m  3
m  AOC   m  1  m  2
m  AOD  m  1  m  2  m  3
O
D
Reasons
Angle Add. Postulate
Angle Add. Postulate
Substitution Prop. Of Eq.
Notice that the To Prove or conclusion is ALWAYS the last statement
8 Given: FL = AT
Prove:
?
FA = LT
F g L
Label diagram to help visualize.
Statements
FL = AT
LA = LA
FL + LA = AT + LA
Reasons
Given
Reflexive Prop. Of Eq.
Add. Prop. Of Eq.
FL + LA = FA
Segment Add. Postulate
AT + LA = LT
Segment Add. Postulate
FA = LT
?
A g T
Substitution Prop. Of Eq.
Notice that the To Prove or conclusion is ALWAYS the last statement
9 Given: DW = ON
?
Prove: DO = WN
O
Label diagram to help visualize.
Statements
DW = ON
g
D
g
W
Reasons
DW = DO + OW
Given
Segment Add. Postulate
ON = ___
OW + ____
WN
Segment Add. Postulate
? N
DO + OW = OW + WN Substitution Prop. Of Eq.
Reflexive Prop. Of Eq.
OW = OW
DO = WN
Subtr. Prop. Of Eq.
Notice that the To Prove or conclusion is ALWAYS the last statement
10 Given:
Prove:
m  4  m  6  180
g
K
+180
m5m6
Label diagram to help visualize.
5?
4
?6
J
Statements
m  4  m  6  180
m  4  m  5  180
m4m5m4m6
L
Reasons
Given
Angle Add. Postulate
Substitution Prop. Of Eq.
m4m4
Reflexive Prop. Of Eq.
m5m6
Subtr. Prop. Of Eq.
Notice that the To Prove or Conclusion is ALWAYS the last statement
11 Given:
m 1 m  2
m 3 m  4
S
Prove: m  SR T  m  ST R
? ?
P
Label diagram to help visualize.
Statements
m 1 m  2
m 3 m  4
Given
4
3
Reasons
1
R
Given
m 1 m  3  m  2  m  4
Add. Prop. Of Eq.
m  1  m  3  m  SR T
Angle Add. Postulate
m  2  m  4  m  ST R
Angle Add. Postulate
m  SR T  m  ST R
Q
Z
Substitution. Prop. Of Eq.
Steps 4 and 5 are needed to permit/validate the substitution.
2
T
12 Given: RP = TQ
S
PS = QS
Prove: RS = TS
RP = TQ
PS = QS
g ?
P
Z
Label diagram to help visualize.
Statements
g
?
Reasons
Given
Given
g
R
RP + PS = TQ + QS
Add. Prop. Of Eq.
RP + PS = RS
TQ + QS = TS
Segment Add. Postulate
Segment Add. Postulate
RS = TS
Substitution. Prop. Of Eq.
Steps 4 and 5 are needed to permit/validate the substitution.
Note that this proof was the same as the previous poof except
for using segments instead of angles.
Q
g
T
13 Given: RQ = TP
ZQ = ZP
S
Prove: RZ = TZ
P
Z
Label diagram to help visualize.
Statements
RQ = TP
?
Reasons
Given
R
RQ = RZ + ZQ Segment Add. Postulate
TP = TZ + ZP Segment Add. Postulate
RZ + ZQ = TZ + ZP Substitution. Prop. Of Eq.
ZQ = ZP
Given
RZ = TZ
Q
?
T
Visually, it is easy to
see that if you
subtract the smaller
segment from the
larger segment the
result will be
obtained
Subtr. Prop. Of Eq.
Notice this is an application of “the sum of the parts equals the whole.”
It is also just like the previous proof.
14 Given: m  SR T  m  ST R
S
m 3 m  4
Prove:
m 1 m  2
P
Label diagram to help visualize.
Statements
m  SR T  m  ST R
Given
4
3
Reasons
1
R
?
m  1  m  3  m  SR T
Angle Add. Postulate
m  2  m  4  m  ST R
Angle Add. Postulate
Substitution. Prop. Of Eq.
m 1 m  3  m  2  m  4
Q
Z
m 3 m  4
Given
m 1 m  2
Subtr. Prop. Of Eq.
2
?
T
C’est fini.
Good day and good luck.