Respuesta :

frika

Answer:

See explanation

Step-by-step explanation:

Consider triangles ADE and CBE. In these triangles,

  • [tex]\overline{AD}\cong \overline{BC}[/tex] - given;
  • [tex]\angle ADE\cong \angle CBE[/tex] - given;
  • [tex]\angle DEA\cong \angle BEC[/tex] - vertical angles.

So, [tex]\triangle ADE\cong \triangle CBE[/tex] by AAS postulate. Congruent triangles have congruent corresponding parts, so

[tex]\overline{DE}\cong \overline{EB}\\ \\\overline{AE}\cong \overline{CE}[/tex]

Since given

[tex]\overline{DE}\cong \overline{CE}\\ \\\overline{AE}\cong \overline{BE},[/tex]

then

[tex]\overline{DE}\cong \overline{EB}\cong \overline{AE}\cong \overline{CE}[/tex]

If diagonals of quadrilateral bisect each other, then this quadrilateral is a rectangle. Hence, ABCD is the rectangle.

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