Draw a diagram and look for the relevant theorems and definitions.
Always
Let's draw a diagram of two intersecting lines and mark two adjacent angles.
What do we know about ∠ 1 and ∠ 2 on the diagram?
They are adjacent angles formed by two intersecting lines, so they form a linear pair.
It is also given that ∠ 1 and ∠ 2 are congruent. According to Right Angle Theorem 2.13, congruent angles that form a linear pair are right angles..
Lines that intersect at a right angle are said to be perpendicular. Thus, it is always true that if two lines intersect to form congruent adjacent angles then the lines are perpendicular.
