SOLUTION: <pre>{{{drawing(200,200,-4,4,-1,5, triangle(-3,0,3,0,0,4), line(-1.5,2,1.5,2), locate(-3.1,0,A), locate(3.1,0,C), locate(-1.9,2.3,D), locate(1.7,2.3,E), locate(0,4.5,B) )}}}

   
             __   __                       __                       __ 
Given: DABC; AB = CB; D is the midpoint of AB; E is the midpoint of BC
Prove: ÐBDE = ÐBED


   Statements        |     Reasons
------------------------------------------
   __    __          |                      __
1. DB = ½AB          | D is the midpoint of AB
   __    __          |                      __
2. EB = ½CB          | E is the midpoint of CB
   __   __           |
3. AB = CB           | given
   __    __          |              __     __
4. EB = ½AB          | Substituting AB for CB, since they are equal by 3
   __   __           |                    __
5. DB = EB           | Both are equal to ½AB by 1 and 4
                     |
6. DDBE is isosceles | Two sides equal by 5
                     |
7. ÐBDE = ÐBED      | Base angles of an isosceles triangle are equal.

Edwin