Answer:
See explanation
Step-by-step explanation:
1. BK is an angle B bisector, then
[tex]\angle ABK\cong \angle CBK[/tex] (definition of angle bisector)
2. BM = MK, then
triangle BMK is isosceles triangle with base BK.
3. Angles adjacent to the base of isosceles triangle are congruent, then
[tex]\angle MBK \cong \angle BKM[/tex]
Note that angle MBK is the same as angle CBK.
4. By substitution property,
[tex]\angle ABK \cong \angle BKM[/tex]
5. By alternate interior angles theorem,
if [tex]\angle ABK \cong \angle BKM[/tex], then [tex]AB\parallel KM[/tex]
