Question

1. in a plane, if two lines are perpendicular to the same line, then they are

to
each other. (parallel, perpendicular, congruent)

1. perpendicular lines

meet at right angles. (always, sometimes, never)

lines intersect to form a right angle, then they are
. (perpendicular, parallel,
use)

Explanation:

Question 8

In a plane, according to the property of lines, if two lines are perpendicular to the same line, their slopes (if we consider coordinate - plane interpretation, for non - vertical lines \(y = mx + c\), the slope of a line perpendicular to a line with slope \(m\) is \(-\frac{1}{m}\)). Let the slope of the common perpendicular line be \(m_0\). The slopes of the two lines perpendicular to it will be the same (both equal to \(-\frac{1}{m_0}\) for non - vertical lines). In general geometric terms (without using coordinate geometry), if two lines are perpendicular to a third line in a plane, they do not intersect each other (since they form the same angle (\(90^{\circ}\)) with the third line), and non - intersecting lines in a plane are parallel.

By the definition of perpendicular lines, two lines are said to be perpendicular if and only if the angle between them is \(90^{\circ}\) (a right angle). So, whenever two lines are perpendicular, they must meet at a right angle. There is no case where perpendicular lines do not meet at a right angle.

The definition of perpendicular lines is that two lines are perpendicular if they intersect at a right angle (\(90^{\circ}\)). Parallel lines do not intersect, and "obtuse" is a property of an angle (\(90^{\circ}<\theta < 180^{\circ}\)) not a property of a pair of lines in the context of intersection to form a right - angle.

Answer:

parallel

Question 9