ABCD and CDEF are two parallelograms constructed on both sides of (CD).
Prove that ABFE is a parallelogram.

ABFE is a parallelogram

Step-by-step explanation: If ABCD uses the same angles (AB) as ABFE does this can only mean that they are equal, therefore they are both parallelograms

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or

step-by-step explanation:

we need to solve for 'x' the following equation:  

we have that:

⇒

⇒ ⇒

factorizing, we get that:

  ⇒

then, the solutions are: or

nothing extraneous has been found!