Question

Reasons

Answer 1

Answer:

(1) The two column proof is presented here as follows;

Statement         ${}$                                Reasons

1. C is the midpoint of $\overline {AE}$         ${}$           Given  

  B is the midpoint of $\overline {AC}$         ${}$          

  D is the midpoint of $\overline {CE}$         ${}$          

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: