Final answer:
An isosceles trapezoid has a midsegment and congruent base angles, but same-side interior angles are not necessarily complementary, so options I and II only apply. Therefore correct option is A
Step-by-step explanation:
The question pertains to the properties of an isosceles trapezoid. An isosceles trapezoid is a quadrilateral with one pair of parallel sides and non-parallel sides that are congruent.
- Midsegment - An isosceles trapezoid has a midsegment, which is a segment that joins the midpoints of the non-parallel sides. This midsegment is parallel to the bases and its length is the average of the two base lengths. So, statement I applies.
- Congruent base angles - The base angles of an isosceles trapezoid are congruent. In other words, each angle adjacent to a base is equal to the angle at the other end of the same base. Therefore, statement II is true.
- For same-side interior angles (the angles between a pair of sides and a transversal intersecting them), it is not generally true that they are complementary, meaning that they add up to 90 degrees. This applies to a trapezoid as well, so statement III does not apply.
Therefore, the correct answer is a. I and II only.