2-7 Proving Segment Relationships

You wrote algebraic and two-column proofs.

• Write proofs involving segment addition.

• Write proofs involving segment congruence.

Ruler Postulate

You must be able to justify everything you do because you are working in a deductive system.

Page 144 in your book

Segment-Addition Postulate

You need to be able to add the lengths of adjacent segments to find the length of longer segments.

Point B is between points A and C if and only if A,B, and C are collinear and

AB + BC = AC.A B C

Page 144 in your book

2. Definition of congruent segmentsAB = CD2.

3. Reflexive Property of EqualityBC = BC3.

4. Segment Addition PostulateAB + BC = AC4.

Statements Reasons

1. 1. GivenAB CD___ ___

6. Segment Addition PostulateCD + BC = BD6.

7. Transitive Property of EqualityAC = BD7.

5. Substitution Property of Equality5. CD + BC = AC

8. Definition of congruent segments8. AC BD___ ___

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 reason correctly completes the proof?

5. ________________AC + CY = AY; BX + XD = BD

5. ?Segment Addition Postulate

Page 145 in your book

Page 146 in your book

Prove the following.

Given:

Prove:

Proof:

Statements Reasons

1. Given1.

2. Transitive Property2.

3. Given3.

4. Transitive Property4.

5. _______________5. ?Symmetric Property

AssignmentPage 147, 1, 2 4, 9, 11