Question

Help Me Please! It's A Multi Choice Question.
ABCD is a square. Given only the choices below, which properties would you use to prove ΔAEB ≅ ΔDEC by ASA?

A. Opposite angles are congruent.
B. All sides are congruent.
C. Opposite sides are | |.
D. The diagonals bisect each other.

Answer 1

Answer:

D

Explanation:

If the diagonals bisect each other, that means BE=EC and AE=ED.  We know that angle AEB= angle CED because they are vertical angles.  We also know that angle ABE and angle DCE are congruent because the shape is a square so its opposite sides are parallel.  If two parrallel sides are cut by a transveral,the transversal being segment BC then alternate interior angles are congruent.  Therefore DCE and ABE are congruent.  We have an angle (the vertical angle) the side (diagonals bisect each other) and we have another angle (alternate interior angles)