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Le pompt de pompt le solve de crime!"
“Indubitably.”
“The proof is in the pudding.”
Je solve le crime. Pompt de pompt pompt."
Deductive Reasoning
2.3 Written Exercises
2.3 Written Exercises
What definition,
postulate, or
theorem justifies
the statement
about the
diagram.
1
A
1 2
B
3 4
D
C
mp
If D is the midpt of BC , then BD  DC .
Definition of midpoint
What definition,
postulate, or
theorem justifies
the statement
about the
diagram.
A
1 2
B
3 4
D
C
2
If 1   2 , then AD is thebi sec tor of  BAC.
Definition of Angle Bisector
What definition,
postulate, or
theorem justifies
the statement
about the
diagram.
A
1 2
B
3 4
D
C
3
If AD is thebi sec tor of  BAC , then 1   2.
Definition of Angle Bisector
What definition,
postulate, or
theorem justifies
the statement
about the
diagram.
4
A
1 2
B
3 4
D
m  3  m  4 180
0
Angle addition postulate
C
What definition,
postulate, or
theorem justifies
the statement
about the
diagram.
5
A
1 2
B
3 4
D
C
If BD  DC , then D is the midpt of BC .
Definition of Midpoint
What definition,
postulate, or
theorem justifies
the statement
about the
diagram.
6
A
1 2
B
3 4
D
C
1
If D is the midpt of BC , then BD  BC .
2
Midpoint Theorem
What definition,
postulate, or
theorem justifies
the statement
about the
diagram.
7
A
1 2
B
3 4
D
m 1  m  2  m  BAC
Angle Addition Postulate
C
What definition,
postulate, or
theorem justifies
the statement
about the
diagram.
8
A
1 2
B
3 4
D
BD + DC = BC
Segment Addition Postulate
C
Write the number that is paired with the
angle bisector  CDE .
C
9
0
180
E
D
Average the numbers to find the middle value.
80  40 120

 60
2
2
Write the number that is paired with the
angle bisector  CDE .
10
C
0
180
E
D
Average the numbers to find the middle value.
120  30 150

 75
2
2
Write the number that is paired with the
angle bisector  CDE .
11
C
0
180
E
D
Average the numbers to find the middle value.
122  18 140

 70
2
2
12
A] draw a pair of angles like below.
B] measure each angle with a protractor.
P
L
m  LMP 120
M
N
m  PMN  60
Note that each number was on the same spot on the protractor.
12
C] What is the measure of the angles
formed by their bisectors?
60 P
60
120
L
M
60 + 30 =
N
0
90
12
D] Explain how you could of known the
answer to part C without measuring the
angles.
60 P
60
120
L
M
N
Half of each portion is half of the whole 1800.
13
The coordinate of points L and X are 16 and 40 respectively.
LN
N is the midpoint of
and Y
Sketch a diagram and find:
Find LN.
is the midpoint of LN .
LX = 40 – 16 = 24
L
16
Y N
X
40
1
LN  LX 12
2
13
The coordinate of points L and X are 16 and 40 respectively.
N is the midpoint of
LN
. Sketch a diagram and find:
Find the coordinate of N.
L
N
X
16
28
40
Why ?
Average the values.
16  40 56
  28
2
2
13
The coordinate of points L and X are 16 and 40 respectively.
N is the midpoint of
LN
. Sketch a diagram and find:
Find coordinate of Y.
Y N
X
16 22 28
40
L
16  28 44
  22
2
2
13
The coordinate of points L and X are 16 and 40 respectively.
N is the midpoint of
Find LY.
LN
. Sketch a diagram and find:
22 – 16 = 6
Y N
X
16 22 28
40
L
14
m  RST  72
SW
bisects  RST and
SZ
bisects  RSW and
Sketch the diagram and find:
R
N
SR
m  RSZ & m  NSZ
720
Z
W
S
bisects  NSW .
T
14
m  RST  72
SW
bisects  RST and
SZ
bisects  RSW and
Sketch the diagram and find:
SR
m  RSZ & m  NSZ
18
R
N
720
Z
18
W
18
36
36
36
S
bisects  NSW .
T
36
15
Suppose that M and N are midpoints of
Which segments are congruent?
M
GH respectively.
GN  NH
L
N
and
LM  MK
K
G
LK
H
15
What additional information would be
needed to conclude LK  GH ?
LM  GN
K
M
L
G
N
H
16
S
R
 RSV   TSV
Suppose
SV
bisects
 RST
And
RU
bisects
 SRT
What angles are congruent?
V
U
T
 SRU   TRU
16
S
 RSV   TSV
 SRU   TRU
R
V
U
T
What additional information would be
needed to show that
VSU  URV
?
 RST   SRT
17
A
What can you deduce
from the given
information.
D
B
E
Given: AE = DE
CE = BE
AC = DB
C
18
A
What can you deduce
from the given
information.
D
Given:
B
E
C
AC bi sec ts DB
DB bi sec ts AC
CE = BE
AC = DB
AE = EC = DE = EB
19
Skip
Complete the proof of Theorem 2-2.
19
Given:
BX
is the bisector of
 ABC
1
Prove: m  ABX  m  ABC
2
BX
is the bisector of
 ABC
m  ABX  m  XBC
Given
Def. of Angle Bisector
m  ABX  m  XBC  m  ABC
Angle Addition Postulate
m  ABX  m  ABX  m  ABC
Substitution
2 m  ABX  m  ABC
1
m  ABX  m  ABC
2
Combine like terms CLT
Division Prop. Of Equality
C’est fini.
Good day and good luck.