Aim: Do Now:

Transcript Aim: Do Now:

Aim: What are the Substitution and Partition
Postulates?
Do Now:
1) Solve the linear system for x and y.
y  3x
2 y  4 x  10
2) If AD  73, AB  4 x  6, BC  2 x  1, and
CD  8 x  2, determine:
a) x
A
B
C
D
b) AB, BC, CD
Geometry Lesson: Partition and
Substitution Postulates
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Partition
Postulate: “A whole is equal to the sum of its parts.”
M
Q
Ex: W C
Or,
Ex:
E
WQ  WC  CM  MQ
WQ  WC  CM  MQ
D
1
2
3
Partition Postulate
Partition Postulate
DEA  1  2  3
Partition Postulate
C
mDEA  m1  m2  m3
Partition Postulate
B
A
Geometry Lesson: Partition and
Substitution Postulates
2
Substitution Postulate:
“A quantity may be substituted for its
equal in any expression.”
Ex:
AB  KL  LM Given
A
B KM  KL  LM Partition Post.
K
L
Ex:
F
E
1
2
4 3
D
C
B
A
M
AB  KM
1  2  3  4
EFC  1  2
CFA  3  4
EFC  CFA
Substitution Post.
Given
Partition Post.
Partition Post.
Substitution Post.
Geometry Lesson: Partition and
Substitution Postulates
3
Example
Given:1:
mAD  mCE
B
Prove: mAB  mCE  mDB
D
A
E
C
Statements
Reasons
1) mAD  mCE
1) Given
2) mAB  mAD  mDB 2) Partition Postulate
3) mAB  mCE  mDB 3) Substitution Postulate
Geometry Lesson: Partition and
Substitution Postulates
4
Given:
Example
2:AEB  CED
A
B
C
Prove: mBED  mAEB  mCED
D
E
Statements
1) AEB  CED
2) mAEB  mCED
3) mBED  mBEC  mCED
4) mBED  mAEB  mCED
Reasons
1) Given
2) Def. congruent angles
3) Partition Postulate
4) Substitution Postulate
Geometry Lesson: Partition and
Substitution Postulates
5
Given:
Example
3:ABC is a right angle
A
ABD  EFH , DBC  HFG
Prove: EFG is a right angle
B
Statements
1)
2)
3)
4)
5)
E
D
ABC is a right angle
mABC  90
ABD  EFH , DBC  HFG
mABD  mEFH , mDBC  mHFG
mABC  mABD  mDBC
6)
mEFG  mEFH  mHFG
7) 90  mABD  mDBC
8) 90  mEFH  mHFG
9) 90  mEFG
Geometry Lesson: Partition and
Substitution Postulates
10)EFG is a right angle
C
H
F
G
Reasons
1)
Given
2)
Def. Rt. angle
3)
Given
Def.  angles
5)
Partition Post.
6)
Partition Post.
7) Subst. Post.
8) Subst. Post.
4)
9)
Subst. Post.
6
10)Def.
Rt. angle
4)
Given:4, 5:AB  2 AD
Example
C
AD  DB
Prove: AB  2 DB
A
5) Given: ma  mb  90
ma  mc
Prove: mc  mb  90
B
D
c b
Geometry Lesson: Partition and
Substitution Postulates
a
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