Question 1150974
given: {{{DB}}} ≆{{{ AC}}}

prove:  {{{AB}}} and {{{CD}}} do not bisect each other

statement........................................reason

1.{{{DB}}} ≆ {{{AC}}} .......................................given

2. ∠ {{{DEB}}}  ≅ to ∠ {{{AEC}}} ...............Intersecting lines form vertical ∠vertical ∠ are ≅.

3. ∠ {{{EDB }}} ≅ to ∠ {{{ECA}}}....alternate ∠ are ≅.

4. ∠ {{{EAC}}}  ≅ to ∠ {{{DBE}}}.............alternate  ∠ are ≅.
 
5. △ {{{DBE}}} is ∽ to △ {{{ACE}}}......... the triangles are similar by Angle-Angle-Angle (AA)

6.  {{{AE}}} ≠ {{{EB}}} and {{{CE}}} ≠ {{{ED}}}, => {{{E}}}  is not midpoint......by definition of midpoint

7. {{{AB}}} and {{{CD}}} do not bisect each other.....by definition of bisector