Is the statement true or false? Explain your reasoning.
Perpendicular lines always intersect at right angles.
i agree
The statement "Perpendicular lines always intersect at right angles" is true.
Perpendicular lines are two lines that intersect at a 90-degree or right angle. To determine if two lines are perpendicular, you can follow these steps:
1. Determine the slopes of the two lines. Slope is a measure of how steep a line is.
2. If the slopes of the two lines are negative reciprocals of each other, then the lines are perpendicular.
For example, consider two lines with slopes m1 and m2. If m1 = 2/3, then the negative reciprocal of m1 would be -3/2. If m2 = -3/2, then the negative reciprocal of m2 would be 2/3. Since the slopes of the two lines are negative reciprocals, the lines are perpendicular.
When two lines are perpendicular, their angles of intersection are always 90 degrees or right angles. Therefore, the statement is true: perpendicular lines always intersect at right angles.