Download Proving Segment Relationships

Proving Segment Relationships
Postulate 2.8 - The Ruler Postulate
• The points on any line or line segment
can be paired with real numbers so
that, given any two points A and B on a
line, A corresponds to zero and B
corresponds to a positive real number.
Proving Segment Relationships
Postulate 2.9 – Segment Addition Postulate
Given three collinear points A, B, and C, if B
is between A and C, then AB + BC = AC.
Likewise, if AB + BC = AC, then B is
between A and C.
Proving Segment Relationships
Theorem 2.2 – Segment Congruence Theorem
Congruence of segments is reflexive, symmetric, and
transitive.
Reflexive: segment AB  segment AB
Symmetric: If segment AB  segment CD, then
segment CD  segment AB.
Transitive: If segment AB  segment CD and
segment CD  segment EF, then segment AB 
segment EF.
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
Prove the following.
Given:
Prove:
Proof:
Statements
Reasons
1.
1. Given
2.
2. Transitive Property
3.
3. Given
4.
4. Transitive Property
5.
5. Symmetric Property