A carpenter must ensure that a large window frame is a recta

A carpenter must ensure that a large window frame is a rectangle. If the corners are labeled E, F, G, and H, the carpenter knows that EF = 51 inches, and FG = 68 inches, GH = 51 inches, and EH = 68 inches. The carpenter could measure the diagonals EG^bar and FH^bar and verify that they are the same length, but chooses 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. EFGH is a parallelogram since _______ Consecutive angles are supplementary by Theorem _______, so angles F, G, and H are also right angles. Therefore, by the _______ Corollary, EFGH is a _______.

Solution

EFGH is a parallelogram since EF=GH, GF=EH and one of the angles between them is 90 degrees proving that they are parallel lines.
According to Consecutive Interior Angles Theorem, If two parallel lines are cut by a transversal, then the pairs of consecutive interior angles formed are supplementary. Here, E is 90 degrees and is the interior angle between the parallel lines, Hence, F,G,H are also right angles.
Therefore, by the rectangle corollary, EFGH is a rectangle.