Given: ABCD is a parallelogram. Prove: ∠1 and ∠2 are supplementary.
Proof:
It is given that ABCD is a parallelogram with angles named, in consecutive order, ∠1 , ∠2 , ∠3, and ∠4.
Opposite angles of a parallelogram are congruent. Thus, ∠1=∠3 and ∠2=∠4 by the definition of congruence.
The sum of the interior angles of any quadrilateral is 360°, so ( I )
Using the substitution property, ∠1+∠1+∠2+∠2=360°.
Therefore, 2(∠1+∠2)=360°.
By the division property of equality, ( II )
Therefore, ∠1 and ∠2 are supplementary.
What statements should go in ( I ) and ( II ) of the proof?