Final answer:
In a parallelogram ABCD with a right angle, the diagonals are congruent because it forms a rectangle whose properties, confirmed by the Pythagorean theorem, dictate that the diagonals must be equal in length, corresponding to option (a).
Step-by-step explanation:
Bao wants to prove that if a parallelogram ABCD has a right angle, then its diagonals are congruent. When dealing with parallelograms, it's important to recognize that a parallelogram with a right angle is a special type of parallelogram called a rectangle. In a rectangle, not only are opposite sides equal in length, but the diagonals are also congruent. This follows from the properties of a rectangle, where the diagonals split it into two right triangles. Using the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides (a² + b² = c²), we can prove that the diagonals are congruent. Since the triangles formed by the diagonals are congruent, the lengths of the hypotenuses (the diagonals) are also congruent. Thus, the correct answer is that the diagonals are equal in length, which corresponds to option (a) 'They are equal in length.'