SOLUTION: Prove that if you draw 3 lines through the point A that crosses the line k, then at least 2 of them are not perpendicular to k

Question 1166383: Prove that if you draw 3 lines through the point A that crosses the line k, then at least 2 of them are not perpendicular to k
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

Name the points of intersection of the lines through A that intersect with line k as B, C, and D. Assume that segment AB is perpendicular to k. Then, since AC and AD are different lines, triangles ABC and ABD are right triangles where AB is one leg and AC and AD are hypotenuses. By the Triangle Inequality AC > AB and AD > AB, but the measure of any line segment that is perpendicular to a line is the shortest distance between the endpoint of the line segment that is not on the line and the line. Since AC and AD are both longer than AB, neither can be a perpendicular.

John

My calculator said it, I believe it, that settles it

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