Which lines are parallel if m<2 = m<8? Justify your answer.
To determine which lines are parallel, we need to identify the lines that have equal slopes (m).
If m<2 = m<8, it means line 2 has the same slope as line 8. Therefore, lines 2 and 8 are parallel.
The justification for this is that when two lines have equal slopes, they will never intersect, meaning they will always remain parallel to each other.
To determine which lines are parallel, we need to know the relationships between the angles formed by the lines. In this case, we are given that the measure of angle 2 (m<2) is equal to the measure of angle 8 (m<8). However, this information is not sufficient to conclude that the lines containing angles 2 and 8 are parallel.
Two lines are parallel if and only if their corresponding angles are congruent (equal). In other words, if the measures of two angles formed by a pair of lines are equal, then the lines are parallel.
In this case, we only have the information that the measures of angles 2 and 8 are equal. Without any additional information, we cannot determine whether the lines containing these angles are parallel.
Therefore, based on the given information, we cannot justify which lines are parallel.
To determine which lines are parallel based on the given information, you need to understand that parallel lines have equal slopes. The slopes of two lines can be compared using their corresponding angle measurements, denoted as m<2 and m<8 in this case.
Here's how you can determine which lines are parallel:
Step 1: Identify the lines being referred to as m<2 and m<8. These could be line segments or lines in a figure.
Step 2: Observe the angle measurements m<2 and m<8. These angles should be associated with the lines mentioned in step 1.
Step 3: Check if m<2 is equal to m<8. If they are equal, the lines associated with these angles will be parallel.
Step 4: Justify your answer by stating that parallel lines have equal slopes, and since m<2 and m<8 are equal, the lines associated with these angles are parallel.
Therefore, the lines corresponding to m<2 and m<8 are parallel if and only if m<2 = m<8.