Question

Diana and Joby wrote the following proofs to prove that vertical angles are congruent. Who is correct?

1) Diana is correct, but Joby is not.
2) Both Diana and Joby are correct.
3) Neither Diana nor Joby is correct.
4) Joby is correct, but Diana is not.

Answer 1

Both Diana and Joby are correct in their proofs that vertical angles are congruent.

Step-by-step explanation:

Vertical angles are angles that share the same vertex but have different rays. In other words, they are opposite angles formed by intersecting lines or line segments. Diana and Joby both wrote proofs to show that vertical angles are congruent, meaning that they have the same measure.

Diana is correct because vertical angles are always congruent. This can be proven using the properties of angles and the fact that vertical angles are formed when two lines intersect.

Joby is also correct because vertical angles are congruent due to the Vertical Angles Theorem, which states that if two lines intersect, the vertical angles formed are congruent. Therefore, both Diana and Joby are correct.