Transcript Lesson 2-7A PowerPoint

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Lesson 2-1 Inductive Reasoning and Conjecture
Lesson 2-2 Logic
Lesson 2-3 Conditional Statements
Lesson 2-4 Deductive Reasoning
Lesson 2-5 Postulates and Paragraph Proofs
Lesson 2-6 Algebraic Proof
Lesson 2-7 Proving Segment Relationships
Lesson 2-8 Proving Angle Relationships
Example 1 Proof With Segment Addition
OBJECTIVE: To write proofs involving segment addition
(2.9.8J) (M8.D.1.1)
Key Concept:
POSTULATE 2.8 – Ruler
Postulate
• The points on any line or line segment can
be paired with real numbers so that, given
any 2 points A and B on a line, A
corresponds to zero, and B corresponds to
a positive real number.
Key Concept:
POSTULATE 2.9: Segment
Addition Postulate.
• If B is between A and C, then AB + BC =
AC.
• If AB + BC = AC, then B is between A and
C.
Prove the following.
Given: PR = QS
Prove: PQ = RS
Proof:
Statements
1. PR = QS
1. Given
2. PR – QR = QS – QR
2. Subtraction Property
3. PR – QR = PQ;
QS – QR = RS
4. PQ = RS
3. Segment Addition
Postulate
4. Substitution
Reasons
Prove the following.
Given:
Prove:
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
5. Segment Addition
Property
6. Substitution
REVIEW
1.
2.
3.
4.
5.
Justify with a property:
Subtraction
If AB = AC + CB, then AB – AC = CB
If mP + m Q = 110 and m R = 110, then m P + m
Q = m R.
Substitution
If x(y + z) = a, then xy + xz = a. Dist. Prop.
If n –17 = 39, then n = 56.
Add. Prop.
If cv = md and md = 15, then cv = 15. Trans. Prop.
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