Prove that
is a right triangle. Select the correct answer from each drop-down menu.

is congruent to
because segment
was constructed so that
.
is congruent to
because segment
was constructed so that
. Since
is a right triangle,
by the
Pythagorean theorem
. We are given that
. Since
and
,
by the
. Also,
by the
. Taking the square root of both sides of the equation gives
. So,
is congruent to
by the definition of congruence. Applying the
,
. By CPCTC,
. Therefore
is a right angle and
is a right triangle.