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  • Prove that two lines that are respectively perpendicular to two intersecting lines intersect each other. [Hint: Use proof by contradiction].

Prove that two lines that are respectively perpendicular to two intersecting lines intersect each other. [Hint: Use proof by contradiction].

Answers (1)

Given: Let lines x and y be two intersecting lines. Let n and p be another two lines which are perpendicular to x and y

To prove: n and p intersect at a point
Proof: Let lines n and p are not intersecting then n \parallel p … (1)
Since n and p are parallel n is perpendicular to x and p is perpendicular to y respectively

So, x \parallel y
But, it is a contradiction as it is given that x and y are two intersecting lines
Thus our assumption is wrong.
n and p intersect at a point

Hence proved

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