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.
Based on the given information, we can determine how lines f and g are related.
Since line f is parallel to line h, they never intersect and have the same slope.
Since lines g and h are perpendicular to line j, line j is the common line at the intersection of lines g and h, and the angle between lines g and h is 90 degrees.
Therefore, lines f and g must also be perpendicular to each other.
This conclusion is based on the fact that if line g is perpendicular to line j and line h is parallel to line f, then the intersection of line g and line h will form a right angle (90 degrees) and will be perpendicular.
Hence, lines f and g are perpendicular to each other.
To determine how lines f and g are related, we need to analyze the given information about the lines:
1. Line f is parallel to line h: This means that lines f and h never intersect and are always equidistant from each other.
2. Lines g and h are perpendicular to line j: This indicates that lines g and h form a right angle with line j. Perpendicular lines intersect at a 90-degree angle.
Now, considering these facts, we can conclude that lines f and g are also perpendicular to each other. Here's how we justify it:
Since line h is parallel to line f and perpendicular to line j, and line g is also perpendicular to line j, it implies that line g is also parallel to line f. This is because if two lines are both perpendicular to a third line, they are parallel to each other.
Hence, based on the given information, we can conclude that lines f and g are perpendicular to each other.
If lines f and h are parallel, and lines g and h are perpendicular, we can conclude that lines f and g are also perpendicular to each other.
This can be justified using the transitive property of perpendicular lines.
Since line f is parallel to line h, and line h is perpendicular to line j, we can say that line f is also perpendicular to line j (by the transitive property).
Similarly, since line g is perpendicular to line j, and line h is also perpendicular to line j, we can conclude that line g and line h are parallel to each other.
Therefore, since line f is perpendicular to line j, and line g is parallel to line h, we can conclude that line f and line g are perpendicular to each other.