Prove That the Slopes of Two Parallel Lines Are Equal

A detailed tutorial on how to prove that the slopes of two parallel lines are equal.

Problem:
Prove that two parallel lines have equal slopes.

Solution to Problem:

The figure below shows two parallel lines L1 and L2. Points A and B are on the line L1 and points C and D are on the line L2.

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Let BM and DN be parallel to the y axis and AM and CN parallel to the x axis. Triangles ABM and CDN have all their corresponding sides parallel are therefore similar. Hence

BM / DN = MA / NC

The above may be written

BM / MA = DN / NC

According to the definition of slope, BM / MA is the slope of line L1 and DN / NC is the slope of L2 and are therefore equal.