How can you determine whether the lines are parallel, without extending these lines? Explain your reasoning.

To determine if two lines are parallel without extending them, you can use the concept of slope. The slope of a line is a measure of its steepness. If two lines are parallel, they will have the same slope.

Here are the steps to determine if two lines are parallel:

1. Find the slope of each line. The slope of a line is usually given by the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are two points on the line.

2. Compare the slopes. If the slopes are equal, then the lines are parallel. If the slopes are not equal, then the lines are not parallel.

Remember, this method assumes that you have enough information to calculate the slope of each line. If you don't have enough information, you may need to use other methods or gather more information.