Deductive Reasoning
“The proof is in the pudding.”“Indubitably.”Je solve le crime. Pompt de pompt pompt."
Le pompt de pompt le solve de crime!"
2.3 Written Exercises
DB C
A
2.3 Written ExercisesWhat definition, postulate, or theorem justifies the statement about the diagram.
, .If D is themidpt of BC then BD DC
Definition of midpoint
1
43
21
mp
DB C
AWhat definition, postulate, or theorem justifies the statement about the diagram.
Definition of Angle Bisector
2
43
21
1 2 , sec .If then ADis thebi tor of BAC
DB C
AWhat definition, postulate, or theorem justifies the statement about the diagram.
Definition of Angle Bisector
343
21
sec , 1 2.If ADis thebi tor of BAC then
DB C
AWhat definition, postulate, or theorem justifies the statement about the diagram.
4
43
21
03 4 180m m Angle addition postulate
DB C
AWhat definition, postulate, or theorem justifies the statement about the diagram.
5
43
21
Definition of Midpoint
, .If BD DC thenDis themidpt of BC
DB C
AWhat definition, postulate, or theorem justifies the statement about the diagram.
6
43
21
Midpoint Theorem
1, .2
If D is themidpt of BC then BD BC
DB C
AWhat definition, postulate, or theorem justifies the statement about the diagram.
7
43
21
Angle Addition Postulate
1 2m m m BAC
DB C
AWhat definition, postulate, or theorem justifies the statement about the diagram.
8
43
21
Segment Addition Postulate
BD + DC = BC
?80
4018
0 0
9
Write the number that is paired with the angle bisector .CDE
C
E
D
80 40 120 602 2
Average the numbers to find the middle value.
?120
3018
0 010
Write the number that is paired with the angle bisector .CDE
C
E
D
120 30 150 752 2
Average the numbers to find the middle value.
?12218
180 0
11
Write the number that is paired with the angle bisector .CDE
C
E
D
122 18 140 702 2
Average the numbers to find the middle value.
12 A] draw a pair of angles like below.B] measure each angle with a protractor.
60m PMN
P
NL M120m LMP
Note that each number was on the same spot on the protractor.
12
P
NL M
120
C] What is the measure of the angles formed by their bisectors?
60
6030
3060
60 + 30 = 900
12
P
NL M
120
60
6030
3060
D] Explain how you could of known the answer to part C without measuring the angles.
Half of each portion is half of the whole 1800.
13
N
The coordinate of points L and X are 16 and 40 respectively.
N is the midpoint of and Y is the midpoint of LN . Sketch a diagram and find:
LN
L X
16 40
Find LN. LX = 40 – 16 = 24
1 122
LN LX
Y
13
N
The coordinate of points L and X are 16 and 40 respectively.
N is the midpoint of . Sketch a diagram and find:LN
L X
16 40
Find the coordinate of N.
16 40 56 282 2
28Why ?
Average the values.
13
N
The coordinate of points L and X are 16 and 40 respectively.
N is the midpoint of . Sketch a diagram and find:LN
L X
16 40
Find coordinate of Y.
28
Y
22
16 28 44 222 2
13
N
The coordinate of points L and X are 16 and 40 respectively.
N is the midpoint of . Sketch a diagram and find:LN
L X
16 40
Find LY.
28
Y
22
22 – 16 = 6
14
Z
bisects and
bisects and bisects .
Sketch the diagram and find:
SW
RST 72m RST SZ
RSW SR
NSW
m RSZ & m NSZ
W
TS
R 720N
bisects and
bisects and bisects .
14
Z
Sketch the diagram and find:
SW
RST
SZ
RSW SR
NSW
m RSZ & m NSZ
W
TS
R 720N
72m RST
36
36
36
18
18
18
36
15
L
G N H
MK
Suppose that M and N are midpoints of and respectively.Which segments are congruent?
LK GH
LM MK
GN NH
15
L
G N H
MK
What additional information would be needed to conclude ?LK GH
LM GN
16
U V
S R
TSuppose bisects And bisects
What angles are congruent?
SV
RST
RU
SRT
RSV TSV
SRU TRU
16
U V
S R
TWhat additional information would be
needed to show that ?
RSV TSV SRU TRU
VSU URV
RST SRT
17E
A
D
B
C
Given:
What can you deduce from the given information.
AE = DE
CE = BE AC = DB
18E
A
D
B
C
Given:
What can you deduce from the given information.
secAC bi ts DBsecDB bi ts AC
CE = BE AC = DBAE = EC = DE = EB
19
Skip
19 Complete the proof of Theorem 2-2.
Given:
Prove:
is the bisector ofBX ABC
12
m ABX m ABC
BX
is the bisector of ABC
m ABX m XBC
m ABX m XBC m ABC
m ABX m ABX m ABC
2m ABX m ABC
12
m ABX m ABC
GivenDef. of Angle Bisector
Angle Addition PostulateSubstitution
Combine like terms CLT
Division Prop. Of Equality
C’est fini.
Good day and good luck.