If two opposite sides of a quadrilateral are perpendicular and congruent, then the quadrilateral is a parallelogram.A.TrueB.False

Question Analysis

To determine whether the statement is true or false, we need to analyze the definition and properties of a parallelogram.

Understanding Parallelograms

1. Definition of Parallelogram: A parallelogram is a quadrilateral with both pairs of opposite sides parallel and equal in length. In addition, opposite angles are equal, and adjacent angles are supplementary.
2. Properties of Opposite Sides: For a quadrilateral to be a parallelogram, it is sufficient to prove that one pair of opposite sides is both congruent and parallel.

Evaluating the Statement

• The statement claims that if two opposite sides are perpendicular (i.e., form a right angle) and congruent, the quadrilateral is a parallelogram.
• However, a quadrilateral formed with two adjacent sides being perpendicular and congruent may not necessarily have the properties of a parallelogram unless both pairs of opposite sides are proven to be parallel as well.

Conclusion

Given that having perpendicular and congruent sides does not guarantee that both pairs of opposite sides are parallel, the statement is False.

Final Answer

B. False