Geometry 1.4 - Segment Proofs

Definition of Midpoint

A----l-----M----l----B

  • With “l” in the middle of both lines, AM=MB

    Segment Addition Postulate

    A----------B-----C

When three points are on a line, AB+BC=AC

Proofs

1. E is the midpoint of DFGiven
2. DE = EF2. Definition of midpoint
3.DE + DE= DE +EF3. Addition Property
4. 2DE= DE+ EF4. Simplify
5. DE + EF = DF5. Segment addition postulate
6. 2DE = DF6. Transitive property
1. WY ≅ YZ, XY ≅ VY1. Given
2. WY = YZ, XY = VY2. Definition of Congruence
3. XY = YZ = XZ3. Segment Addition Postulate
4. VY + YZ = XZ4. Substitution Property
5. VY = YW = VW5. Segment Addition Postulate
6. XZ = VW6. Transitive Property
7. XZ ≅ VW7. Definition of Congruence

A------B--C-------D

AB ≅ CDGiven
AB = CDDefinition of congruence
AC + CD = ADSegment Addition Postulate
AB + BD = ADSegment Addition Postulate
AB + BD = AC + CDTransitive Property
BD = ACSubtraction Property