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.

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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.

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