Geometry crime investigation

Question

Some thief has taken a necklace from old Mrs. Hexagon. The culprit ran

off very fast, but not before some bystanders got a look at the culprit.

Witness 1 (Mrs. Hexagon) -- "It all happened so fast! All I can tell you is

that the thief had congruent diagonals."

Witness 2 -- "As this individual was fleeing the scene of the crime, I saw a

pair of parallel sides. I did not get a look at the other pair of sides, so I'm

not sure if there were two pairs or not."

Witness 3 -- "I did not notice if the sides were parallel or not, but I saw a

pair of opposite sides that were definitely not congruent."

Answer 1

Since cannot be sure both pairs of sides are parallel or not, the thief is not a parallelogram. Since one pair of sides is parallel and a pair of opposite sides are not congruent, the thief is a trapezoid. Furthermore, since the diagonals are congruent, the thief is an isosceles trapezoid.