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, FG = 68 inches GH = 51 inches, and EH = 68 inches. The carpenter could measure the diagonals EG and FT and verify right they are the same length, but chooses another approach. After verifying and 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 opposite sides are congruent (EF=GH),(EH=FG). consecutive angles are supplimentry by theorem:

that if the two lines are parallel, then the consecutive interior angles are supplementary to each other.

So, angles F,G,H are right angles. Therefore, by the property if one angle is right angle then other angles will also be right angle. Corollary EFGH is a parallelogram