Final answer:
The question does not provide the actual proofs written by Diana and Joby to determine who is correct about vertical angles being congruent. Without this information, their correctness cannot be assessed. However, perpendicular lines form 90-degree angles, not 270 degrees, and the Pythagorean theorem can calculate the resultant vector length of two perpendicular vectors.
Step-by-step explanation:
The question provided does not contain sufficient information for us to determine who, between Diana and Joby, wrote a correct proof proving that vertical angles are congruent. In mathematics, specifically in geometry, vertical angles are angles opposite each other when two lines cross. They are congruent, meaning they have the same angle measure. A correct proof would typically involve stating that when two lines intersect, they form two pairs of opposite, congruent angles due to the intersecting lines being straight lines and the angles around a point summing up to 360 degrees.
To determine the correctness of a proof, we would need to see the logical steps and justifications each person used rather than unrelated statements. Correct proofs require clear reasoning and use of geometric principles. Therefore, without the content of Diana's and Joby's proofs, it is impossible to declare who is correct.
However, if we refer to the provided information, statement (d) 'They are perpendicular, forming a 270° angle between each other' is incorrect as perpendicular lines form 90° angles, not 270°. Furthermore, the Pythagorean theorem can indeed be used to calculate the length of the resultant vector when adding two vectors at right angles to each other, as the vectors form a right-angled triangle, and the theorem applies.