Final answer:
Both Kasey's reasoning about right angles in the triangles and Emma's reasoning about the triangles being congruent because of the ASA criterion are valid. Therefore, a diagonal does indeed partition a rectangle into two congruent right triangles.
Step-by-step explanation:
Kasey and Emma are both correct in their reasoning about the triangles formed by a diagonal of a rectangle. Kasey believes that each triangle will have a right angle because a rectangle has four right angles, and this is true. When a diagonal of a rectangle is drawn, it cuts the rectangle into two right triangles. The right angle of the rectangle becomes the right angle for both triangles.
Emma states that a diagonal will always partition a rectangle into two congruent triangles. Her reasoning about the diagonal acting as a transversal between parallel lines and satisfying the ASA criterion is also valid. The congruent angles at each end of the diagonal and the equal lengths of the diagonal itself ensure by Angle-Side-Angle congruence that the triangles are congruent.
The answer to the student's question is A. Both Kasey and Emma's reasoning is valid.