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EFGH is a parallelogram. In EFGH, line EG is perpendicular to line FH. which conclusion is incorrect?

A. EFGH is a rectangle
B. EFGH is a square

1 Answer

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Final answer:

The incorrect conclusion is that EFGH is a square, since there is no information provided about the lengths of the sides. To be a square, a parallelogram must have four sides of equal length in addition to having four right angles, which is not confirmed in the given question.

Step-by-step explanation:

The question involves a geometric figure, a parallelogram named EFGH, where line EG is perpendicular to line FH. Given this information, we need to identify which conclusion is incorrect about the parallelogram being a rectangle or a square. A rectangle is a parallelogram with four right angles, and a square is a parallelogram with four right angles and four sides of equal length.

If line EG is perpendicular to line FH in a parallelogram, this implies that all angles in the parallelogram are right angles, since opposite angles in a parallelogram are congruent, and alternating angles between parallel lines are also congruent. Therefore, EFGH meets the criteria of being a rectangle because all angles are right. However, not enough information is provided to confirm that all sides are of equal length, which is a requirement for EFGH to be a square. Since the problem does not state that all sides are equal, we cannot conclude that EFGH is a square; this could be the incorrect conclusion if the sides are not equal.

Keep in mind that for a parallelogram to be classified as a square, we need confirmation that all sides are of equal length along with all angles being right angles. If the statement about EFGH being a square assumes equal sides without evidence, then it is the incorrect conclusion.

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