Question

Two lines l and m are perpendicular to the lines n and p respectively. If n and p intersect , then prove that l and m also intersect.

Answer 1

Answer:

The proof is explained step wise below :

Step-by-step explanation:

Given : Let n & p be two intersecting lines.

Let l ⊥ n & m ⊥ p.

To prove : l & m will intersect.

Proof :

Let n and p be two intersecting lines. Let us assume that l and m do not intersect.

Now l ⊥ n. [ given] I ║ m [ by assumption]

Therefore, m ⊥ n ......(1)

And , m ⊥ p ....,..(2)

From 1 &2 we have n ║ p which is wrong since n & p intersect. [ Given]

Hence our assumption is wrong .

l & m intersect .

Hence Proved.