Note: Your teacher will grade your response to ensure you receive proper credit for your answers.
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 m∠4 = m∠5, then angle 6 and angle 7 would be parallel.
An angle is considered parallel to another angle when they are on the same side of the transversal line (in this case, line l) and the corresponding angles are congruent.
In this case, angle 6 and angle 7 are both above line s and left of line m, making them on the same side of line l. If m∠4 = m∠5, then angle 6 and angle 7 would have congruent measures, which means they are parallel.