(1) The two column proof is presented here as follows;
Statement
Reasons
1. C is the midpoint of
Given
B is the midpoint of
D is the midpoint of
2. AC = CE, AB = BC, CD = DE
Definition of midpoint
3. AB + BC = AC, CD + DE = CE
Segment addition postulate
4. CD + DE = AC
Substitution property of equality
5. AB + BC = CD + DE
Substitution property of equality
6. BC + BC = CD + CD
Substitution property of equality
7. 2·BC = 2·CD
Addition of two identical quantities
8. BC = CD
Division property of equality
9. BC ≅ CD
Definition of Congruence
(2) The two column proof for the triangular geometric figure is presented here as follows;
Statement
Reasons
1. 2·WV = XY; 2·YZ = XW; WV = YZ
Given
2. 2·WV = 2·YZ
Multiplication property
3. XY = XW
Substitution Property
4. XW + WV = XV
Segment Addition Property
XY + YZ = XZ
5. XW + WV = XV
Substitution Property
XW + WV = XZ
6. XV = XZ
Substitution Property
Explanation: