Is the following statement true or false? Perpendicular lines form a 90° angle.
The correct answer and explanation is:
The statement “Perpendicular lines form a 90° angle” is true.
Perpendicular lines are defined as two lines that intersect to form right angles. A right angle is exactly 90 degrees. This means that when two lines are perpendicular, they meet or cross each other in such a way that the angle between them is a right angle.
In geometry, angles are measured in degrees, with a full circle having 360 degrees. A right angle is one quarter of a full circle, which is why it measures 90 degrees. The concept of perpendicularity is fundamental in mathematics, especially in geometry, because it helps in understanding shapes, coordinate systems, and many properties of figures.
For example, on a Cartesian coordinate plane, the x-axis and y-axis are perpendicular to each other, and their intersection forms four right angles of 90 degrees each. This perpendicular relationship is essential for defining coordinates, plotting points, and analyzing geometric figures.
Furthermore, perpendicular lines have many practical applications in everyday life. Construction and engineering rely on perpendicularity to ensure that buildings, walls, and other structures are correctly aligned and stable. In art and design, creating perpendicular lines helps produce balanced and aesthetically pleasing compositions.
To summarize, perpendicular lines always meet at a right angle, which is exactly 90 degrees. This fact is a fundamental property in geometry and is widely used in various fields involving measurements, construction, and design.