Lines f, g, h and j are in the same plane. Line f is parallel to line h. Lines g and h are perpendicular to line j. Using this information how are lines f and g related? Justify your answer.(2 points)
Based on the given information, we can conclude that lines f and g are perpendicular to each other.
This is because line f is parallel to line h, and line h is perpendicular to line j. If two lines are parallel to the same line, they must be parallel to each other. Similarly, if one of the lines perpendicular to a second line, and the second line is perpendicular to a third line, then the first and third lines are also perpendicular to each other.
Therefore, since line f is parallel to line h and line h is perpendicular to line j, we can conclude that line f and line g are perpendicular to each other.
Based on the given information, lines f and h are parallel, and lines g and h are perpendicular to line j.
If g is perpendicular to j and h is also perpendicular to j, then g and h are parallel to each other. Therefore, f is also parallel to g.
To summarize, lines f and g are parallel to each other.
To determine the relationship between lines f and g, we need to analyze the given information:
1. Lines f and h are parallel.
2. Lines g and h are perpendicular to line j.
From the first piece of information, we know that lines f and h never intersect and are always equidistant. This means that the angles between line f and any line perpendicular to line h will be equal.
From the second piece of information, we know that lines g and h are perpendicular to line j. Therefore, the angle between lines g and h is 90 degrees.
Since lines f and h are parallel, and the angle between lines g and h is 90 degrees, we can conclude that lines f and g are also perpendicular. This is because any line perpendicular to line h will also be perpendicular to line f, based on the fact that they are parallel.
Hence, lines f and g are perpendicular to each other.