Question

Help!! i only know how to prove it’s a parallelogram and that’s it

Answer 1

See explanation

Explanation:

Consider triangles ADE and CBE. In these triangles,

• 
  `\overline{AD}\cong \overline{BC}` - given;
• 
  `\angle ADE\cong \angle CBE` - given;
• 
  `\angle DEA\cong \angle BEC` - vertical angles.

So,
`\triangle ADE\cong \triangle CBE` by AAS postulate. Congruent triangles have congruent corresponding parts, so

`\overline{DE}\cong \overline{EB}\\ \\\overline{AE}\cong \overline{CE}`

Since given

`\overline{DE}\cong \overline{CE}\\ \\\overline{AE}\cong \overline{BE},`

then

`\overline{DE}\cong \overline{EB}\cong \overline{AE}\cong \overline{CE}`

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