Answer :
Given this geometry question, let's examine the statement in detail.
The statement given is: "If two angles of a triangle are congruent, then the sides opposite those angles are congruent."
To address this, we need to reference a fundamental geometric principle known as the Isosceles Triangle Theorem. This theorem is crucial in determining the correctness of the statement.
Here are the steps to understand why the statement is true:
1. Definition of Congruent Angles: When two angles are congruent, they have the same measure. In a triangle, if two angles are congruent, let us denote them as ∠A and ∠B.
2. Opposite Sides of Congruent Angles: In a triangle, each angle is opposite a unique side. Suppose ∠A is opposite side 'a', and ∠B is opposite side 'b'.
3. Isosceles Triangle Theorem: This theorem states that in an isosceles triangle, the sides opposite the equal angles are equal. This is because the angles opposite equal sides in a triangle are also equal. So, if ∠A = ∠B, then by the theorem, side 'a' must be equal to side 'b'.
4. Conclusion: Since we have established that if two angles are congruent (as per the given statement), the sides opposite these angles must also be congruent.
Thus, the correct answer to the question is:
A. True
Therefore, the sides opposite the two congruent angles in a triangle must indeed be congruent.
The statement given is: "If two angles of a triangle are congruent, then the sides opposite those angles are congruent."
To address this, we need to reference a fundamental geometric principle known as the Isosceles Triangle Theorem. This theorem is crucial in determining the correctness of the statement.
Here are the steps to understand why the statement is true:
1. Definition of Congruent Angles: When two angles are congruent, they have the same measure. In a triangle, if two angles are congruent, let us denote them as ∠A and ∠B.
2. Opposite Sides of Congruent Angles: In a triangle, each angle is opposite a unique side. Suppose ∠A is opposite side 'a', and ∠B is opposite side 'b'.
3. Isosceles Triangle Theorem: This theorem states that in an isosceles triangle, the sides opposite the equal angles are equal. This is because the angles opposite equal sides in a triangle are also equal. So, if ∠A = ∠B, then by the theorem, side 'a' must be equal to side 'b'.
4. Conclusion: Since we have established that if two angles are congruent (as per the given statement), the sides opposite these angles must also be congruent.
Thus, the correct answer to the question is:
A. True
Therefore, the sides opposite the two congruent angles in a triangle must indeed be congruent.
