Download Since the lines are perpendicular, they form a right angle by

Perpendicular Lines Biconditional Theorem
Lines are perpendicular if and only if they form
four congruent, adjacent, right angles.
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PARAGRAPH
PROOF
Since the lines are perpendicular,
they form a right angle by definition.
As vertical angles are congruent, another angle is right
since an angle congruent to a right angle must be right.
An adjacent angle is right because it is supplementary to
a right angle with which it forms a linear pair.
A fourth angle is right because it is supplementary to one,
as well as vertical, and congruent, to a right angle.
Conversely, if four adjacent angles are congruent,
they have equal measures summing 360° in total.
Therefore, each angle is 360°÷4, or a 90° right angle, and
the sides of each angle are perpendicular by definition.