The proposition is true since square products are squares. However, the converse (“If ab is a perfect square, then a and b are perfect squares”) is false; for example, 2 × 8 = 16.
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Both the proposition and its converse (“If a + x = a + y, then x = y”) are true. Adding equals preserves equality and subtracting a from both sides restores x = y.
Both the proposition and its converse (“If corresponding angles formed by a transversal are equal, then the lines are parallel”) are true, representing fundamental geometric properties defining parallel line relationships.