Question

prove that two lines that are respectively perpendicular to two intersecting lines intersect each other .​

Answer 1

Answer:

If n and p are any two intersecting lines.

Draw two lines such that l⊥n andm⊥p

To prove: Lines l andm will intersect.

Proof:

Let n and p be two intersecting lines.

Let us assume that l and m do not intersect each other.

Now l⊥n (Given)

Let us assume that l⊥m

Therefore, m⊥n ...(1)

But given that m⊥p ...(2)

From (1) and (2), we get n∥p

But given, lines n and p intersect each other.

Hence, our assumption is wrong.

Answer 2

Step-by-step explanation:

If n and p are any two intersecting lines.

Draw two lines such that l⊥n andm⊥p

To prove: Lines l andm will intersect.

Proof:

Let n and p be two intersecting lines.

Let us assume that l and m do not intersect each other.

Now l⊥n (Given)

Let us assume that l⊥m

Therefore, m⊥n ...(1)

But given that m⊥p ...(2)

From (1) and (2), we get n∥p

But given, lines n and p intersect each other.

Hence, our assumption is wrong.

Therefore l and m intersect each other.