Upload
lyndon
View
56
Download
0
Embed Size (px)
DESCRIPTION
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. - PowerPoint PPT Presentation
Citation preview
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