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'?

Option 1: Angle Addition Postulate
Option 2: Corresponding Angles Postulate
Option 3: Vertical Angles Theorem
Option 4: Alternate Exterior Angles Theorem

Answer 1

The Vertical Angles Theorem justifies that angle BAD is congruent to angle CAD if segment AD is perpendicular to segment BC, making them both right angles and hence congruent. In a proof, if segment AD is perpendicular to segment BC, the reason that justifies the statement angle BAD is congruent to angle CAD is the Vertical Angles Theorem.

Step-by-step explanation:

If segment AD is perpendicular to segment BC, then angle BAD is congruent to angle CAD because when a line is perpendicular to another line, it forms two congruent adjacent angles that are both right angles at the intersection. The reason that justifies this statement is the Vertical Angles Theorem, which states that the angles opposite each other when two lines cross are congruent. Hence, Option 3: Vertical Angles Theorem is the correct answer to justify the congruency of angles BAD and CAD when AD is perpendicular to BC.