Question

in which quadrilateral are the diagonals always congruent? rectangle rhombus trapezoid parallelogram

Explanation:

To determine in which quadrilateral the diagonals are always congruent, we analyze each option:

• Rectangle: By the properties of a rectangle, its diagonals are always congruent. This is a fundamental property of rectangles (since a rectangle is a parallelogram with right angles, and the congruence of diagonals can be proven using triangle congruence, e.g., in rectangle \(ABCD\), triangles \(ABC\) and \(DCB\) are congruent by SAS, leading to \(AC = BD\)).
• Rhombus: The diagonals of a rhombus are perpendicular bisectors of each other but are not necessarily congruent (except in the special case of a square, which is a type of rhombus and rectangle).
• Trapezoid: In a general trapezoid, the diagonals are not necessarily congruent. Only in isosceles trapezoids are the diagonals congruent, but the question asks for a quadrilateral where diagonals are always congruent, and trapezoids (in general) do not satisfy this.
• Parallelogram: In a general parallelogram, the diagonals bisect each other but are not necessarily congruent (e.g., in a non - rectangular parallelogram like a rhombus that is not a square, or a slanted parallelogram, the diagonals have different lengths).

Answer:

A. rectangle