To answer the question about whether the sides opposite congruent angles in a triangle may not be congruent, let’s analyze the properties of triangles, particularly isosceles triangles.
1. Understanding Triangle Congruence:
- In any triangle, if two angles are congruent (equal in measure), the definition of geometric properties states that the sides opposite these angles must also be congruent. This is a derived property from the isosceles triangle theorem.
2. Isosceles Triangle Theorem:
- The isosceles triangle theorem states that in an isosceles triangle, the angles opposite the congruent sides are congruent. This also works in reverse: if two angles in a triangle are congruent, the triangle is isosceles, indicating that the sides opposite these congruent angles are themselves congruent.
3. Analyzing the Statement:
- The statement given is: "If two angles of a triangle are congruent, then the sides opposite those angles may not be congruent."
- According to the properties discussed, this statement would mean that we are claiming the sides opposite the congruent angles might not be equal, which contradicts the isosceles triangle theorem.
4. Conclusion:
- Since the isosceles triangle theorem confirms that the sides opposite congruent angles in a triangle are always congruent, the given statement is incorrect.
Thus, the correct answer to the question "If two angles of a triangle are congruent, then the sides opposite those angles may not be congruent" is:
○ B. False
