A Comprehensive Guide to Diagonals in Quadrilaterals | Intersection, Division, and Right Angles Explained

Diagonals bisect each other at right angles (90°)

In geometry, a diagonal refers to a line segment that connects two non-adjacent vertices of a polygon

In geometry, a diagonal refers to a line segment that connects two non-adjacent vertices of a polygon. When we say that diagonals bisect each other at right angles (90°), it means that the diagonals of a quadrilateral (a polygon with four sides) intersect at a point, and the intersection point divides each diagonal into two equal parts. Moreover, the angle formed by the intersection of the diagonals is a right angle, measuring 90 degrees.

To better understand this concept, let’s consider a square as an example. In a square, the diagonals are line segments connecting opposite corners of the square. If we draw both diagonals within the square, they will intersect at a point in the middle of the square. At that point of intersection, each diagonal is divided into two equal parts, and the angle formed is a right angle.

If you have a different type of quadrilateral, such as a rhombus, rectangle, or kite, the diagonals will still bisect each other at right angles. One important property to note is that this property holds true only for quadrilaterals and not for other polygons. It is specific to the nature of quadrilaterals.

To summarize, when we say that diagonals bisect each other at right angles in a quadrilateral, it means that the diagonals of the shape intersect at a point, dividing each diagonal into two equal segments. Additionally, the angle formed at the point of intersection is a right angle, measuring 90 degrees.

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