The image contains a figure in which angles and sides are named, some data is given, and the proof is to be provided.
Every proof starts with the given data.
Thus, from the options, we select those containing the information provided:
a) BD is parallel to CE
d) Angle 5 is congruent to angle 6
Now we can see the segments AB and AD have one tick mark. This means they are congruent or have the same measure.
AB is congruent to AD
The triangle ABD, having two equal sides, is isosceles. Every isosceles triangle has two congruent angles, in this case, angles 5 and 6.
Thus, the next step in the proof is:
c) Angle 5 is congruent to C and angle 6 is congruent to E
Because of the transitive property of congruence, it follows:
e) Angles C and D are congruent
Being two angles in a triangle congruent, it follows the triangle is isosceles, thus:
b) AC and AE are congruent
This is the final step of the proof