Question

Given the following, determine which lines, if any are parallel. State the postulate or theorem that justifies your answer.1. ∠1 ≊∠32. ∠2 ≊ ∠54. m∠6 + m∠8 = 180

Answer 1

1) Given that angle 1 and angle 3 are congruent, it means that they are corresponding angles. Two angles are corresponding if they have similar positions and lie on the same side of the transversal cutting across two parallel lines. Thus, the transversal is line l and the parallel lines are lines j and k

2) Given that angle 2 and angle 5 are congruent, it means that they are alternate angles. Two angles are alternate if they have similar positions and lie on opposite side of the transversal cutting across two parallel lines. Thus, the transversal is line l and the parallel lines are lines j and k

4) If angle 6 and angle 8 = 180, this is so because angle 6 and angle 10 are corresponding angles and thus, they are congruent. Angle 10 and angle 8 are linear pairs. It means that their sum is 180. Thus, angle 6 + angle 8 = 180

Since they are corresponding angles, the parallel lines are l and m