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Which lines are parallel if mangle4 = mangle5? Justify your answer.
An image with four lines that intersect in pairs is shown.
Lines r is above line s. Lines r and s each intersect lines l and m.
line l is left of line m.
8 angles are labeled with numbers.
Angle 1 is above line r and left of line l.
Angle 2 is above line r and right of line l.
Angle 3 is below line r and left of line l.
Angle 4 is below line r and right of line l.
Angle 5 is above line s and left of line l.
Angle 6 is above line s and right of line l.
Angle 7 is above line r and left of line m.
Angle 8 is below line r and left of line m.
(2 points)
If mangle4 = mangle5, it means that Angle 4 is congruent to Angle 5.
Since Angle 5 is above line s and left of line l, and Angle 6 is above line s and right of line l, we can conclude that line l is parallel to line s.
Therefore, line r is also parallel to line m because lines r and s each intersect lines l and m.
So, the lines that are parallel are line l and line s.
If m∠4 = m∠5, this means that Angle 4 and Angle 5 are congruent.
Looking at the image, we see that Angle 4 is below line r and right of line l, while Angle 5 is above line s and left of line l.
Since these angles are not on the same line and do not share any sides, they cannot be parallel lines.
Therefore, there are no lines that are parallel if m∠4 = m∠5.
To determine which lines are parallel, we need to find pairs of angles that have equal measures. When two lines are intersected by a transversal, alternate interior angles are congruent, corresponding angles are congruent, and consecutive interior angles are supplementary.
Given that m∠4 = m∠5, we need to find pairs of angles that have equal measures.
Looking at the image, we can see that angle 2 and angle 5 are both above line r and left of line l. Since alternate interior angles are congruent, we can conclude that line r is parallel to line s.
Therefore, lines r and s are parallel.