Question

if $\angle abe = 100\degree$ and $\angle edc = 100\degree$, are the two triangles, $\triangle abe$ and $\triangle edc$ similar? if so, by what criterion?
a yes, by aa criterion
b yes, by sas criterion
c yes, by ssa criterion
d no, not possible to tell.

Explanation:

1. First, identify vertical angles: $\angle AEB$ and $\angle DEC$ are vertical angles, so $\angle AEB = \angle DEC$.
2. Given $\angle ABE = 100^\circ$ and $\angle EDC = 100^\circ$, so $\angle ABE = \angle EDC$.
3. By the AA (Angle - Angle) similarity criterion, if two angles of one triangle are equal to two angles of another triangle, the triangles are similar. Here, we have two pairs of equal angles ($\angle ABE=\angle EDC$ and $\angle AEB = \angle DEC$), so $\triangle ABE \sim \triangle EDC$ by AA criterion.

Answer:

A. yes, by AA criterion