Question

In a proof, what is the reason that justifies this statement: If segment AD is perpendicular to segment BC, angle BAD is congruent to angle CAD.

a) Perpendicular angles theorem
b) Corresponding angles postulate
c) Vertical angles theorem
d) Alternate interior angles theorem

Answer 1

The reason that justifies the statement "If segment AD is perpendicular to segment BC, angle BAD is congruent to angle CAD" is the Vertical angles theorem. According to the Vertical angles theorem, when two lines intersect, the angles that are opposite to each other (vertical angles) are congruent.

Step-by-step explanation:

In a proof, the reason that justifies the statement "If segment AD is perpendicular to segment BC, angle BAD is congruent to angle CAD" is the Vertical angles theorem. According to the Vertical angles theorem, when two lines intersect, the angles that are opposite to each other (vertical angles) are congruent. In this case, angle BAD and angle CAD are vertical angles because they are formed by the intersection of segments AD and BC.