1
�
�
�
�
Prove:
�
DBC
�
�
1
Proof:
1.
__
›
BD
is the angle bisector of
�
ABC
.
1. Given
2.
�
ABD
�
�
DBC
2. Def. of
�
bisector
3.
�
ABD
�
�
1
3. Given
4.
�
DBC
�
�
1
4. Transitive Prop. of
�
1. Given:
N
is the midpoint of
_
MP
,
Q
is the
midpoint of
_
RP
, and
_
PQ
�
_
NM
.
�
�
�
�
�
Prove:
_
PN
�
_
QR
Write a justification for each step.
Proof:
1.
N
is the midpoint of
_
MP
.
1.
Given
2.
Q
is the midpoint of
_
RP
.
2.
Given
3.
_
PN
�
_
NM
3.
Def. of midpoint
4.
_
PQ
�
_
NM
4.
Given
5.
_
PN
�
_
PQ
5.
Transitive Prop. of
�
6.
_
PQ
�
_
QR
6.
Def. of midpoint
7.
_
PN
�
_
QR
7.
Transitive Prop. of
�

Copyright © by Holt, Rinehart and Winston.
71
Holt Geometry
All rights reserved.
Copyright © by Holt, Rinehart and Winston.
51
Holt Geometry
All rights reserved.
LESSON
1.
Use the given flowchart proof to complete the two-column proof.
Given:
m
�
BAC
�
m
�
EAF
, m
�
CAD
�
m
�
DAE
�
�
�
�
�
�
Prove:
m
�
BAD
�
m
�
DAF
�
�
���
�
�
��
�
���
��
�
�
���
�
�
��
�
���
�����
�
�
���
�
�
��
�
���
�
�
��
�
���
��
�
�
���
�
�
��
�
���
�
�
��
�
���
�
�����������
�
�
���
�
�
��
�
���
�
�
��
�
�
���
�
�
��
�
���
��������������
�
�
�
���
�
�
��
�
���
������
Statements
Reasons
1. m
�
BAC
�
m
�
EAF
, m
�
CAD
�
m
�
DAE
1.
a.
Given
2.
b.
m
�
BAC
�
m
�
CAD
�
m
�
EAF
�
m
�
DAE
2. Add. Prop. of
�
3. m
�
BAC
�
m
�
CAD
�
m
�
BAD
,
m
�
EAF
�
m
�
DAE
�
m
�
DAF
3.
�
Add. Post.
4. m
�
BAD
�
m
�
DAF
4.
c.
Subst.
2.
Miguel breaks a 17-centimeter-long pencil into two pieces. One of the pieces is
9 centimeters long. Use the given paragraph proof to complete the two-column
proof showing that the other piece is 8 centimeters long.
Given:
AC
�
17,
AB
�
9
9
�
�
�
17
Prove:
BC
�
8
By the Segment Addition Postulate, the sum of
AB
and
BC
equals
AC
. That is,
AB
�
BC
�
AC
. It is given that
AC
�
17 and
AB
�
9. Substitution leaves the
equation 9
�
BC
�
17. Using the Subtraction Property of Equality to take 9
away from both sides shows that
BC
�
8.
Statements
Reasons
1.
AB
�
BC
�
AC
1.
a.
Seg. Add. Post.
2.
AC
�
17,
AB
�
9
2. Given
3.
b.
9
�
BC
�
17
3. Subst.
4.
c.
BC
�
8
4. Subtr. Prop. of
�
2-7
Practice A
Flowchart and Paragraph Proofs
Copyright © by Holt, Rinehart and Winston.
52
Holt Geometry
All rights reserved.
LESSON
1.
Use the given two-column proof to write a flowchart proof.
�
�
�
�
Given:
�
4
�
�
3
Prove:
m
�
1
�
m
�
2
Statements
Reasons
1.
�
1 and
�
4 are supplementary,
�
2 and
�
3 are supplementary.
1. Linear Pair Thm.
2.
�
4
�
�
3
2. Given
3.
�
1
�
�
2
3.
�
Supps. Thm.
4. m
�
1
�
m
�
2
4. Def. of
�
�
�
������
�
����������������������
�
������
�
��������������������
��������������
�
�
��
�
��
�
�
��������
�
�
�
�
��
�
�
�
�
�
������������
�
��
�
�
�

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