Which of the following statements is true about isosceles trapezoids? I. The diagonals are congruent II. Both pairs of base angles are congruent. II. The opposite sides are congruent N. The bases of a trapezoid are congruent. I, II, III only I and II only Il and IV only I and III only

To determine which statements about isosceles trapezoids are true, let's analyze each statement one by one. 1. **Statement I: The diagonals are congruent.** - This statement is true for isosceles trapezoids. In an isosceles trapezoid, the non-parallel sides (legs) are equal in length, which results in the diagonals being congruent. 2. **Statement II: Both pairs of base angles are congruent.** - This statement is also true. In an isosceles trapezoid, the angles adjacent to each base are equal, meaning both pairs of base angles are congruent. 3. **Statement III: The opposite sides are congruent.** - This statement is false. In an isosceles trapezoid, only the non-parallel sides (the legs) are congruent, while the bases (the parallel sides) are not necessarily equal. 4. **Statement IV: The bases of a trapezoid are congruent.** - This statement is false. In an isosceles trapezoid, the bases are parallel but not necessarily congruent. Now, let's summarize the truth values of the statements: - I: True - II: True - III: False - IV: False Based on this analysis, the true statements are I and II only. Thus, the correct answer is **I and II only**.