Warm Up:
If AC ≅ BD, how can you show that AB ≅ CD
E
Statements
Reasons
B
A
C
D
F
Subtraction Postulate: If equal quantities are subtracted from equal quantities, the differences are equal.
**We will still need to use the Partition and Substitution Postulates!!
1) AC ≅ BD
2) BC ≅ BC
3) AB + BC = AC, CD + BC = BD
4) AB + BC ≅ CD + BC
5) AB ≅ CD
1
E
1
~
ABE =
2
A
B
C
D
Statements
Reasons
1)
1) Given
2)
2) Given
3) AB + BC ≅ AC,
DC + BC ≅ DB
4)
3) Partition Postulate
4) Given
5) AB + BC ≅ DC + BC
6) BC ≅
BC
~
ABE =
5) Substitution Postulate
6) Reflexive Property
7) Subtraction Postulate
7) AB ≅ DC
8)
DCE
DCE
2
F
Given: ABCD
FA AD
AD ED
AF ≅ DE
AC ≅ BD
D
A
B
C
E
Prove: ABF ≅ CED
Statements
Reasons
1)
1) Given
2)
2) Given
3) <FAB and <EDC
are right angles
3) Perpendicular lines
intersect at right angles
4) <FAB ≅ <EDC
4) All right angles are congruent
5)
5) Given
6) Partition Postulate
7)
8) 9) BC ≅ BC
10) AB ≅ DC
11)
7) Given
8) Substitution Postulate
9) Reflexive Property
10) Subtraction Postulate
11) 3
4
Given: Prove: 5
6