Which statement best defines perpendicular lines?
A.
lines that lie in the same plane
B.
lines that intersect and form right angles
C.
lines that lie in the same plane and do not intersect
D.
lines that share a point
The Correct Answer and Explanation is :
The correct answer is B: lines that intersect and form right angles.
Explanation:
Perpendicular lines are defined as two lines that meet (or intersect) at a right angle, which is exactly 90 degrees. This relationship is crucial in geometry and is a fundamental concept when working with shapes, angles, and other geometric figures.
Key points:
- Right angle: A right angle measures 90 degrees. When two lines meet at this angle, they are considered perpendicular.
- Intersection: Perpendicular lines must intersect at a single point. If the lines do not meet, they cannot be perpendicular.
- Planes and orientation: While perpendicular lines can exist within the same plane (as in 2D geometry), they can also exist in different planes (in 3D geometry), but for them to be perpendicular, the intersection must form a 90-degree angle.
Why the other options are incorrect:
- Option A: Lines that lie in the same plane: This is a description of coplanar lines, not necessarily perpendicular. Coplanar lines can be parallel or intersect at angles other than 90 degrees.
- Option C: Lines that lie in the same plane and do not intersect: This describes parallel lines, not perpendicular ones. Parallel lines never meet, and thus cannot form a right angle.
- Option D: Lines that share a point: This is a general description of lines that intersect but does not specify that the lines form a right angle. Two lines that share a point could intersect at any angle, not necessarily 90 degrees.
In summary, perpendicular lines specifically refer to lines that intersect at a right angle, forming an essential concept in both two- and three-dimensional geometry.