Geoffrey wrote the following paragraph proof showing that rectangles are parallelograms with congruent diagonals.
according to the given information, quadrilateral rect is a rectangle.
by the definition of a rectangle, all four angles measure 90°.
segment er is parallel to segment ct and segment ec is parallel to segment rt by the converse of the same-side interior angles theorem.
quadrilateral rect is then a parallelogram by definition of a parallelogram.
now, construct diagonals et and cr. because rect is a parallelogram, opposite sides are congruent.
therefore, one can say that segment er is congruent to segment ct.
segment tr is congruent to itself by the reflexive property of equality.
the says triangle ert is congruent to triangle ctr.
and because corresponding parts of congruent triangles are congruent (cpctc), diagonals et and cr are congruent.