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Difficulty: EasyProperties of Quadrilaterals

Is the following statement true or false? In any rectangle, the diagonals must be perpendicular to each other.

Answer: Answer

Answer

False
The correct answer is False because the diagonals of a rectangle are perpendicular only when the rectangle has equal side lengths (making it a square). In a standard rectangle, the diagonals are congruent and bisect each other, but they do not intersect at right angles.

Step-by-Step Solution

1
Analyze the properties of a general rectangle.
A rectangle is a parallelogram with four right angles. Its diagonals are congruent and bisect each other.
To determine diagonal behavior, we must start with the standard properties of the shape.
2
Examine if the diagonals are perpendicular in all cases.
The diagonals of a rectangle are perpendicular only if the rectangle is a square (all sides equal). For a general rectangle with unequal adjacent sides, the diagonals are not perpendicular.
A single counterexample, such as a rectangle with unequal adjacent sides, shows that the property does not hold universally.

Key Concept

Properties of rectangle diagonals
Estimated Time:45s
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Topics

Properties of Quadrilaterals

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