A trapezoid is a quadrilateral whose two sides are parallel. In the figure below, is a trapezoid and
is parallel to
. In this post, we are going to prove that in a trapezoid, the consecutive angles between a pair of parallel sides are complementary. That is, we are going to prove in the figure above that
degrees and
.
The Trapezoid Angle Theorem.
In a trapezoid, the consecutive angles between a pair of parallel sides are complementary.
Proof
Extend line segment at
and locate point
on the extended part as shown above. Label the angles angles as 1 and 2.
because they are a linear pair.
because they are corresponding angles of the parallel lines containing
and
.
by substitution.
and
are supplementary by definition of supplementary angles.