proving segment relationships
DESCRIPTION
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). Lesson 7 MI/Vocab. AC. A. B. C. 5. 8. AB. BC. Segment Addition Postulate. - PowerPoint PPT PresentationTRANSCRIPT
Proving Segment Proving Segment RelationshipsRelationships
• 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.
A B CAC
AB BC5 8
13
If AB = 5 and BC = 8, then AC = 5 + 8 = 13.
Segment Addition Postulate
If AB = 3x + 2
BC = 5x – 3
AC = 15
Solve for x.
A B C
AB + BC = AC
(3x + 2) + (5x – 3) = 15
8x –1 = 15
8x = 16
x = 2
Proof with Segment Addition
1. GivenPR = QS1.
2. Subtraction PropertyPR – QR = QS – QR2.
3. Segment Addition Postulate
PR – QR = PQ; QS – QR = RS
3.
4. SubstitutionPQ = RS4.
Proof:Statements Reasons
Prove the following.
Given: PR = QSProve: PQ = RS
Prove the following.
Given: AC = ABAB = BXCY = XD
Prove: AY = BD
1. GivenAC = AB, AB = BX1.
2. Transitive PropertyAC = BX2.
3. GivenCY = XD3.
4. Addition PropertyAC + CY = BX + XD4.
AY = BD 6. Substitution6.
Proof:Statements Reasons
Which choice correctly completes the proof?
5. ________________AC + CY = AY; BX + XD = BD
5. ?Segment Addition
Proof with Segment Congruence
Prove the following.
Given:
Prove:
5. Symmetric Property5.
Proof:Statements Reasons
1. Given1.
2. Definition of congruent segments
2.
3. Given3.
4. Transitive Property4.
Prove:Given:
Proof with Segment Congruence
Prove the following.
Given:
Prove:
Which choice correctly completes the proof?
Proof:Statements Reasons
1. Given1.
2. Transitive Property2.
3. Given3.
4. Transitive Property4.
5. _______________5. ?Symmetric Property
HomeworkHomework
Chapter 2-7Chapter 2-7
• Pg 121Pg 121
1 – 3, 16, 19 – 291 – 3, 16, 19 – 29