Question

A rectangular sheet of newspaper is folded as shown in the figure. The two triangles formed are ______.

• A. not congruent, as the orientation is flipped
• B. not congruent, as the corresponding sides are of unequal length
• C. congruent as the orientation does not matter
• D. None of the above

Answer 1

The correct option is C congruent as the orientation does not matter

Let the triangles formed be $△$ABC and $△$CDA

In triangles, $△$ABC and $△$CDA
CA = AC = a (diagonal; common side)
AB = CD (opposite sides of a rectangle)
BC = DA (opposite sides of a rectangle)

$\therefore △ABC\cong △CDA$
by SSS criterion for congruency of triangles

So, irrespective of orientation, the two triangles formed after folding the sheet of newspaper diagonally are congruent.