How do we know that EDFC is a rectangle?

Right Triangle

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The definition of a rectangle is a quadrilateral with four right angles. From this we can prove that the opposite sides of a rectangle are equal in length.

Since ED is parallel to CB, and angle ACB is a right angle, by corresponding angles we can conclude that angle AED is a right angle.

If AED is a right angle, then by virtue of the sum of the angles of a transversal equaling pi, we can conclude that CED is a right angle.