Diagonal line through rectangle always creates two congruent triangles (?)

Question

1) Is it true that the diagonal line through a rectangle always creates to congruent triangles?

2) If a quadrilateral has two right angles that are opposite (is this the right word to use), as shown, then it's necessarily a rectangle?

Answer 1

$a)$ the triangles are congruent by the $LLL$ criterion.

$b)$ No, consider the drawing.

Answer 2

For part (b) if you first draw the line segment HK, and then make a circle with that as a diameter, then one can choose the points J,I anywhere on the two semicircles which the circle is cut into by HK (on opposite sides of HK), and they will make the desired right angles. This clearly allows the final result to fail to be a rectangle.