From a Parallelogram to a Rectangle: Identifying and defining elements

Looking at triangle DAE, we are given that DA equals DE, therefore the triangle is isosceles.

As a result, angles DAE and DEA are both equal to 45 degrees.

Now let's calculate angle D:

We know that the sum of angles in a triangle is 180 degrees, and since we have two angles of 45 degrees:

$D+45+45=180$

$D+90=180$

$D=180-90$

$D=90$

Since angle D is a right angle, the parallelogram is indeed a rectangle, according to the rule that if one angle in a parallelogram is a right angle, the parallelogram is a rectangle.

Let's calculate angle A:

$92+33=125$

The parallelogram in the diagram is not a rectangle since angle A is greater than 90 degrees, and in a rectangle all angles are right angles.

The parallelogram in the drawing cannot be a rectangle because in a rectangle all angles are right angles, meaning they are equal to 90 degrees.

Angle A is greater than 90 degrees.

Let's calculate angle B:

$64+26=90$

The parallelogram in the drawing is indeed a rectangle since a parallelogram with at least one right angle is a rectangle.