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prove that two lines that are respectively perpendicular to two intersecting lines intersect each other (use contradiction method).please answer fast​

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6th

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Basic Geometrical Ideas

Types of Lines

Prove that the two lines th...

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

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ANSWER

GIVEN:-N and P be two intersect lines .

Let lL⊥N andM⊥P

TO PROVE: L andM will intersect.

PROOF:

Let n and and p be two intersect lines.

Let us assume that I and m do not intersect.

Now I⊥N (given)

I⊥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 .

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