Question

1. which of the following statements regarding perpendicular lines is true?

a. perpendicular lines form four angles that add up to 180 degrees
b. perpendicular lines intersect to form four right angles
c. perpendicular lines never intersect and have no points in common
d. perpendicular lines are always horizontal and vertical

Explanation:

• Option A: When two lines are perpendicular, the sum of the four angles formed is \(360^{\circ}\) (since the sum of angles around a point is \(360^{\circ}\)), not \(180^{\circ}\). So, this option is incorrect.
• Option B: By the definition of perpendicular lines, when two lines are perpendicular, they intersect at \(90^{\circ}\) angles. And since there are four angles formed at the intersection of two lines, all four angles are right angles (\(90^{\circ}\)). This option is correct.
• Option C: Perpendicular lines do intersect. In fact, they intersect at a right - angle. Lines that never intersect and have no points in common are parallel lines. So, this option is incorrect.
• Option D: Perpendicular lines are not always horizontal and vertical. For example, a line with a slope of \(m_1 = 2\) and a line with a slope of \(m_2=-\frac{1}{2}\) are perpendicular (since \(m_1\times m_2=- 1\)), but they are not horizontal and vertical. So, this option is incorrect.

Answer:

B. perpendicular lines intersect to form four right angles