Is the quadrilateral  DEFG a parallelogram? Demonstrate  all your work to justify your answer. 

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durbanville eNotes educator| Certified Educator

In order for the quadrilateral DEFG to be a parallelogram, we will use the properties of a parallelogram.

The opposite angles of a parallelogram are equal to each other so to prove - or disprove:

`/_D_(1) = 110` degrees - given

`therefore /_D_(2) = 70` degrees -angles on a straight line=180 degrees

`/_F=65` degrees - given

and angle F is opposite angle `D_(2)`

but `/_F!=/_D_(2)`


Therefore DEFG is NOT a parallelogram