A carpenter must ensure that a large window frame is a rectangle. If the corners

Question

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, FG = 68 inches, GH = 51 inches, and EH = 68 inches. The carpenter could measure the diagonals EG and FH 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 _____.

Explanation / Answer

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.

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