Right angle

Right angle

Perpendicular-coloured

Rtriangle

Triangle 30-60-90 rotated

Right angle is a fundamental concept in geometry, particularly in Euclidean geometry, where it plays a critical role in definitions, theorems, and practical applications. A right angle is formed when two lines or line segments intersect in such a way that the four angles formed at the intersection are equal. Each of these angles measures 90 degrees (90°), making them equal to one quarter of a full turn. The symbol for a right angle is a small square placed at the vertex of the angle.

Definition

In mathematics, more specifically in Euclidean geometry, a right angle is defined as an angle of exactly 90 degrees (90°), representing one-quarter of a full circle. The concept of a right angle is one of the most fundamental in geometry, serving as the basis for various geometric constructions, properties, and theorems. When two lines intersect at a right angle, they are said to be perpendicular to each other. This perpendicularity is a key concept in defining and understanding right angles.

Properties

A right angle has several important properties that distinguish it from other types of angles:

• It is one of the basic types of angles, alongside acute and obtuse angles.
• Two lines or segments that intersect at a right angle are said to be perpendicular.
• In a right triangle, one of the angles is a right angle. This property is crucial in the study of trigonometry.
• The concept of right angles is used to define rectangles, squares, and other geometric shapes that feature perpendicular sides.

Measurement

The measurement of a right angle is universally accepted as 90 degrees. In other systems of angle measurement, a right angle is also defined as π/2 radians, 100 grads, or one-quarter of a full turn. The choice of unit depends on the context in which the angle is being measured or used.

Applications

Right angles are ubiquitous in both theoretical and practical aspects of geometry. They are fundamental in the design and construction of buildings, furniture, and various tools and devices. The concept of perpendicularity, which arises from right angles, is crucial in ensuring stability and balance in construction and design. In addition, right angles play a significant role in navigation, graphic design, and various fields of engineering and mathematics.

See also

• Angle
• Perpendicular
• Right triangle
• Euclidean geometry
• Trigonometry