The missing reason is AAS Congruence Theorem

You can simply say AAS for short, and your teacher will likely know what you mean.

The AAS stands for Angle Angle Side. It refers to the fact how we can use two pairs of congruent angles, and a side that is not between the angles, to prove two triangles are congruent.

In this case, ABE = CDE are the two congruent 90 degree angles, and AEB = DEC are the two vertical angles

The two congruent sides are shown by the tickmarks, so AB = CD. In other words, this information is given.

Keep in mind that AAS is slightly different from ASA, so the order matters.

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