Question

what is a perpendicular line?

Answer 1

so they create four right angles EVERY time?

Answer 2

A perpendicular line is a line that intersects another line at a right angle (90 degrees). When two lines are perpendicular, they create four right angles at the point of intersection. In a Cartesian coordinate system, if you have a line with a certain slope, a line that is perpendicular to it will have a slope that is the negative reciprocal of the original line's slope. For example, if one line has a slope of \( m \), a line that is perpendicular to it will have a slope of \( -\frac{1}{m} \), provided \( m \) is not zero.

In geometry, understanding perpendicular lines is essential for constructing shapes and understanding angles within various contexts, such as proofs and theorems involving triangles, rectangles, and many other geometric figures.

Answer 3

Yes, when two lines are perpendicular to each other, they always intersect to create four right angles at the point of intersection. This is true in a two-dimensional plane.

Here's how it works:

1. When two lines intersect at a right angle (90 degrees), they create four angles.
2. Each of these angles measures 90 degrees, which is the definition of a right angle.
3. The four angles comprise the total angle around the intersection point, which is 360 degrees (4 angles × 90 degrees = 360 degrees).

Therefore, at the intersection of two perpendicular lines, there are always four right angles formed.