The answer is
Converting this into a geometry problem requires us to name the points. Let give the home plate a symbol A, first base will be B, second base will be C, and the third base will be D. Now, we can present a geometrical proof:
STATEMENTS | REASONS
(1) BC = CD | Given
m(2) AC = AC | Reflexive Property
(3) triangle ACD = triangle ACB | SAS Congruence
(4) AD = AB | CPCTC
when CPCTC means Congruent Parts of Congruent Triangles are Congruent.
Therefore, the distance from first base to home plate, and from home plate to third plate are equal.