Embed Size (px)
DESCRIPTION
1) Solve the linear system for x and y. a) x. A. B. C. D. b) AB, BC, CD. What are the Substitution and Partition Postulates?. Do Now:. Aim:. Ex:. W. C. M. Q. Or,. Partition Postulate. Ex:. D. 1. E. C. 2. 3. B. Partition Postulate. A. Partition Postulate:. - PowerPoint PPT Presentation
Citation preview
1Geometry Lesson: Partition and Substitution Postulates
Aim:
1) Solve the linear system for x and y.3
2 4 10
y x
y x
A B C D
2) If 73, 4 6, 2 1, and
8 2, determine:
AD AB x BC x
CD x
a) x
b) AB, BC, CD
What are the Substitution and Partition Postulates?
Do Now:
2Geometry Lesson: Partition and Substitution Postulates
Partition Postulate: “A whole is equal to the sum of its parts.”Ex: W C M Q
Partition Postulate
Partition PostulateOr, WQ WC CM MQ
Ex:
123
D
C
B
A
E
DEA 1 2 3 Partition Postulate
1 2 3m DEA m m m Partition Postulate
WQ WC CM MQ
3Geometry Lesson: Partition and Substitution Postulates
Substitution Postulate:“A quantity may be substituted for its equal in any expression.”
Ex:A B
ML
K
AB KL LM Given
AB KM Substitution Post.
Ex:
123
D
C
B
A
E
4F
1 2EFC Partition Post.
3 4CFA Partition Post.
1 2 3 4 Given
EFC CFA Substitution Post.
KM KL LM Partition Post.
4Geometry Lesson: Partition and Substitution Postulates
Example 1:
A
B
C
D E
Given:
Prove:
mAD mCE
mAB mCE mDB
Statements Reasons
1) 1)
2) 2)
3) 3)
GivenmAD mCEmAB mAD mDB Partition Postulate
mAB mCE mDB Substitution Postulate
5Geometry Lesson: Partition and Substitution Postulates
Example 2:Given:
Prove:
Statements Reasons
1) 1)
2) 2)
3) 3)
4) 4)
Given
Partition Postulate
Substitution Postulate
A BC
DE
AEB CED
m BED m AEB m CED
AEB CED m AEB m CED Def. congruent angles
m BED m BEC m CED m BED m AEB m CED
6Geometry Lesson: Partition and Substitution Postulates
Example 3:
Statements Reasons1) 1)
2) 2)
3) 3)
4) 4)
5) 5)
6) 6)
7) 7)
8) 8)
9) 9)
10) 10)
Given is a right angleABC
Given90m ABC Def. Rt. angle
m ABC m ABD m DBC Partition Post.
,ABD EFH DBC HFG ,m ABD m EFH m DBC m HFG Def. angles
Given:
Prove:
is a right angleABC A
CB
E
F G
D H
is a right angleEFG,ABD EFH DBC HFG
m EFG m EFH m HFG Partition Post.90 m ABD m DBC Subst. Post.90 m EFH m HFG Subst. Post.
90 m EFG Subst. Post. is a right angleEFG Def. Rt. angle
7Geometry Lesson: Partition and Substitution Postulates
Example 4, 5:4) Given:
Prove:
A
C
BD
2AB AD
AD DB
2AB DB
5) Given:
Prove: a
90m a m b m a m c
90m c m b bc
