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
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.