No, the diagonals of all parallelograms are not congruent.
A parallelogram is defined as a four-sided figure (quadrilateral) with opposite sides that are parallel and equal in length. While it is true that the diagonals of a rectangle (a specific type of parallelogram) are congruent, this property does not hold for all parallelograms.
To illustrate, let’s consider the common types of parallelograms:
- Rectangle: Both diagonals are equal in length and bisect each other. Thus, they are congruent.
- Rhombus: The diagonals of a rhombus are not equal in length, but they do bisect each other at right angles.
- General Parallelogram: In most generic parallelograms, the diagonals will vary in length, and though they bisect each other, they are not necessarily equal.
In conclusion, while rectangles have congruent diagonals, the diagonals of other types of parallelograms, such as rhombuses and general parallelograms, are not necessarily equal, meaning not all parallelograms have congruent diagonals.