Question

In Euclidean (standard) geometry, prove: If two lines share a common perpendicular, then the lines are parallel. (You do not need to use axioms of Euclidean geometry in this exercsise, you can use all the standard knowledge about geometry.)

Answer 1

Explanation:

Standard knowledge about geometry.

Lines can be described as y=mx+b where m is the slope of the line...(1)

Perpendicular lines have perpendicular slopes. Perpendicular slopes are negative reciprocals of each other...(2)

Two lines are parallel ⇔ they have the same slope...(3)

Check the image to read the proof........