Answer:
From top to bottom:
A, J, E, B, I, C, D, G, F, H
See below for more clarification.
Step-by-step explanation:
We are given that AB is parallel to CD, XY is the perpendicular bisector of AB, and E is the midpoint of XY. And we want to prove that ΔAEB ≅ ΔDEC.
Statements:
1) XY is perpendicular to AB.
Definition of perpendicular bisector.
2) XY ⊥ CD.
In a plane, if a transveral is perpendicular to one of the two parallel lines, then it is perpendicular to the other.
3) m∠AXE = 90°, m∠DYE = 90°.
Definition of perpendicular lines.
4) ∠AXE ≅ ∠DYE.
Right angles are congruent.
5) XE ≅ YE
Definition of a midpoint.
6) ∠A ≅ ∠D.
Alternate Interior Angles Theorem
7) ΔAEX ≅ ΔDEY
AAS Triangle Congruence*
(*∠A ≅ ∠D, ∠AXE ≅ ∠DYE, and XE ≅ YE)
8) AE ≅ DE
Corresponding parts of congruent triangles are congruent (CPCTC).
9) ∠AEB ≅ ∠DEC
Vertical Angles Theorem
10) ΔAEB ≅ ΔDEC
ASA Triangle Congruence**
(**∠A ≅ ∠D, AE ≅ DE, and ∠AEB ≅ ∠DEC)
and 
is given as 
, where
is the vertical distance between two points on the y-axis
is the horizontal distance between two points on the x-axis