1.AD=EC | Seg. Sub. Postulate
You don't need the reflexive prop stuff, just go straight to this.
ad = ec by cpctc probably
edit: cpctc stands for congruent parts of congruent triangles are congruent so im 90% sure thats it
if that was an actual property (i've never seen this before) it wouldve made my 9th grade geometry A TON easier.