Prove that the two lines that are respectively perpendicular to two intersecting lines intersect each other.

Let L and M be perpendicular to N and P respectively. Let us assume that L and M do not intersect. If they do not intersect that means they are parallel

We have L⊥N (given)

We have L||M (by assumption)

Therefore, M⊥N           ……..(1)

And , M⊥P         ……….(2)

From (1) and (2) we have N∥P is wrong since N and P intersect (given)

Hence, our assumption is wrong . So L and M intersect