Transcript Geo – Ch 2-7 Proving Segment Relationships

Proving Segment
Relationships
• Write proofs involving segment addition.
• Write proofs involving segment congruence.
Standard 4.0 Students prove basic theorems
involving congruence and similarity. (Key)
Segment Addition Postulate
• If B is b/t A and C, then AB + BC = AC.
• If AB + BC = AC, then B is b/t A and C.
AC
13
A
B
AB
5
C
BC
8
If AB = 5 and BC = 8, then AC = 5 + 8 = 13.
Segment Addition Postulate
A
If AB = 3x + 2
BC = 5x – 3
AC = 15
Solve for x.
B
C
AB + BC = AC
(3x + 2) + (5x – 3) = 15
8x –1 = 15
8x = 16
x=2
Proof with Segment Addition
Prove the following.
Given: PR = QS
Prove: PQ = RS
Proof:
Statements
Reasons
1. PR = QS
2. PR – QR = QS – QR
1. Given
3. PR – QR = PQ;
QS – QR = RS
4. PQ = RS
3. Segment Addition
Postulate
4. Substitution
2. Subtraction Property
Prove the following.
Given: AC = AB
AB = BX
CY = XD
Prove: AY = BD
Which choice correctly completes the proof?
Proof:
Statements
Reasons
1. AC = AB, AB = BX
1. Given
2. AC = BX
2. Transitive Property
3. CY = XD
3. Given
4. AC + CY = BX + XD
4. Addition Property
5. AC + CY = AY;
BX + XD = BD
6. AY = BD
Segment
5. ________________
? Addition
6. Substitution
Proof with Segment Congruence
Prove the following.
Given:
Prove:
Proof with Segment Congruence
Given:
Proof:
Statements
Prove:
Reasons
1.
1. Given
2.
3.
2. Definition of congruent
segments
3. Given
4.
4. Transitive Property
5.
5. Symmetric Property
Prove the following.
Given:
Prove:
Which choice correctly completes the proof?
Proof:
Statements
Reasons
1.
1. Given
2.
2. Transitive Property
3.
3. Given
4.
4. Transitive Property
5.
Symmetric
? Property
5. _______________
Homework
Chapter 2-7
• Pg 121
1 – 3, 16, 19 – 29