An example of a shape with congruent diagonals is a rectangle.
Congruent Diagonals Explained
Congruent diagonals are diagonals within a polygon (a closed shape with straight sides) that are of equal length. Certain quadrilaterals, which are four-sided polygons, are known for having this property.
Quadrilaterals with Congruent Diagonals
The most common examples of quadrilaterals with congruent diagonals are:
-
Rectangle: A rectangle is a quadrilateral with four right angles. Because of this, its diagonals are always congruent. The diagonals also bisect each other, meaning they cut each other in half.
-
Square: A square is a special type of rectangle where all four sides are equal in length. Since a square is also a rectangle, its diagonals are congruent and bisect each other at right angles.
-
Isosceles Trapezoid: An isosceles trapezoid is a trapezoid (a quadrilateral with at least one pair of parallel sides) where the non-parallel sides are equal in length. The diagonals of an isosceles trapezoid are congruent.
Why Congruent Diagonals Matter
The presence of congruent diagonals is a defining characteristic that helps classify these quadrilaterals and is useful in geometric proofs and constructions.
