Part 1
we have that
If AE=CE
then the triangle AEC is an isosceles triangle
so
has two equal sides and two equal interior angles
therefore
Part 2
we have that
triangle ADE is an isoceles triangle
therefore
DA=DE
Part 3
we have that
triangle BDF is an isosceles triangle
therefore
DF=BF
Part 4
ABC is an isosceles triangle
therefore