Final answer:
The mathematical property demonstrated by the statement 'If H = K and K = J, then H = J' is the Transitive Property of Equality.
Step-by-step explanation:
The mathematical property showcased in the statement "If H = K and K = J, then H = J" is the Transitive Property of Equality. This property asserts that if one quantity is equal to a second quantity, and the second quantity is equal to a third quantity, then the first and third quantities must also be equal.
Widely applied in algebra and geometry, the Transitive Property plays a pivotal role in establishing equalities within proofs and solutions, facilitating a logical and consistent progression in mathematical reasoning.