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, hut chooses another approach. Alter verifying that angle E is a right angle the carpenter insists that EFGH must he 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 ingles F, G, and H are also right angles. Therefore, by the Corollary. EFGH is a

Explanation / Answer

EFGH is a parallelogram since it has 4 sides and opposite sides are congruent (Theorem 8.9).

Consecutive angles are supplementary by Theorem 8.5 so angles F,G and H are also right angles. Therefore by the rectangle corrolary EFGH is a rectangle.

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