Answer :
Ted's claim is correct - the two shaded triangles must be congruent.
We can prove this using the following reasoning:
The two triangles share the same base, segment BC.
The two triangles have the same height, as the height of a triangle is measured as a perpendicular line from the base to the opposite vertex, and the perpendicular line from B to segment AD is the same length as the perpendicular line from C to segment AE.
Therefore, the two triangles have the same area.
If two triangles have the same area and share a common side (in this case, segment BC), they must be congruent by the Side-Area-Side (SAS) congruence theorem.
Therefore, we can conclude that the two shaded triangles are congruent.
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