Question

Look at the following below. Which of the following statements could be used to prove that vertical angles are congruent?

a) APC ~ DPB because angles complementary to the same angle are congruent to each other.
b) APC ~ DPB because angles supplementary to the same angle are congruent to each other.
c) APC ~ DPB because angles adjacent to the same angle are congruent to each other.
d) APC ~ DPB because the angles formed by the same pair of intersecting lines are congruent to each other.

Answer 1

The statement that proves vertical angles are congruent is that the angles formed by the same pair of intersecting lines are congruent to each other.

Step-by-step explanation:

The correct statement that could be used to prove that vertical angles are congruent is (d) APC ≅ DPB because the angles formed by the same pair of intersecting lines are congruent to each other. When two lines intersect, they form two pairs of vertical angles, which are across from each other. These angles are always congruent, which means they have the same measure. Two triangles are congruent if all three corresponding sides and their corresponding angles are equal.