Is this statement true or false? The Area Congruence Postulate states that if two polygons have the same area, then the polygons are congruent. false

**True or False Statement:** > *The Area Congruence Postulate states that if two polygons have the same area, then the polygons are congruent.* **Your Answer:** False **Evaluation:** **Correct** --- **Explanation:** The statement is **false**. **Reasons:** 1. **Definition of Congruence:** - **Congruent Polygons**: Two polygons are congruent if they have the same shape **and** size. This means one can be transformed into the other via rigid transformations such as translations, rotations, and reflections. - **Area Equality**: While having the same area is a necessary condition for congruence, it is **not sufficient**. Polygons can have identical areas but different shapes, making them non-congruent. 2. **Counterexample:** - **Rectangle vs. Rhombus**: Consider a rectangle and a rhombus, both with an area of 12 square units. Despite having the same area, unless all corresponding sides and angles are equal, these two shapes are not congruent. 3. **Area Congruence Postulate Clarification:** - There isn't a widely recognized "Area Congruence Postulate" in standard geometry. Congruence is typically established through side-side-side (SSS), side-angle-side (SAS), and other such criteria, not merely area. **Conclusion:** Having the same area does **not** guarantee that two polygons are congruent. Therefore, the statement is false.