Decide if the following statement is true:
Two concurrent lines can never be perpendicular.
Explain why or why not?
If you define concurrent lines as three or more lines that meet at a single point, they can be perpendicular, but they do not have to be.
To determine if the statement "Two concurrent lines can never be perpendicular" is true or false, we need to understand what is meant by "concurrent lines" and "perpendicular lines."
1. Concurrent lines: Concurrent lines are lines that pass through the same point. In other words, they intersect at a common point.
2. Perpendicular lines: Perpendicular lines are two lines that intersect at a right angle (90 degrees). When two lines are perpendicular, the product of their slopes is -1.
Now, let's prove or disprove the statement:
Suppose we have two concurrent lines, Line A and Line B, that intersect at point P.
If Line A and Line B are perpendicular, then the angle formed by the two lines at point P must be 90 degrees.
To verify this, we need to check the slopes of Line A and Line B. If the product of their slopes is -1, then they are indeed perpendicular.
However, since the statement claims that two concurrent lines can never be perpendicular, we must prove the statement false by finding an example where two concurrent lines are perpendicular.
Consider Line A passing through point P (0,0) and having a slope of 1. This means that any point on Line A will have coordinates (x, x), where x is the same value for both the x and y coordinates.
Now, let's consider Line B passing through point P (0,0) and having a slope of -1. This means any point on Line B will have coordinates (x, -x).
If we plot these lines on a graph, we will see that both Line A and Line B intersect at point P (0,0), making them concurrent lines. Additionally, it is evident that Line A and Line B are perpendicular to each other since they form a right angle at point P.
Therefore, the statement "Two concurrent lines can never be perpendicular" is false. There are cases where two concurrent lines can indeed be perpendicular.