State which lines, segments, or rays are parallel in the figure and state the postulate or theorem which proves them parallel. Thank you for your help.
In the given diagram, put a point at the upper part of the ray heading upwards, and label it X. Similarly, put a point at the lower part of the ray heading downwards, label it Y.
From the diagram, `m/_MLX` = 28+42 = 70 degrees
and `m/_KJL` = 38+32 = 70 degrees
Therefore `/_MLX`= `/_KJL`
Here, LM and JK are two line segments and XY is their transversal, intersecting them in such a way that the corresponding angles, `/_MLX` and `/_KJL` are equal.
Therefore, according to the corresponding angles postulate “If two lines and a transversal form equal corresponding angles, then the lines are parallel” these two line segments are parallel.
i.e. LM ll KJ.
There is no other pair of lines in the diagram which are parallel.