Question

A carpenter must ensure that a large window frame is a rectangle. If the corners are labled E,F,G, and H, the carpenter knows that EF=51 inches, FG=28 inches, GH=51 inches, and EH=28 inches. The carpenter could measure the diagonals EG and FH and verify that they are the same length, nut choose another approach. After verifying that angle E is a right angle the carpenter insists that EFGH must be a true rectangle. Finish the reasoning outlined below to justify the carpenter's logic.

1)EFGH is a parallelogram since__________________________.
2)consecutive angles are supplementary by Therom______, so angles F,G, and H are also right angles.
3)Therfore, by the ______________ Corollary, EFGH is a _________________.