Question

if l, m, n, are three lines such that l paralell m and n perpendicular, then prove that n perpendicular m​

Answer 1

Answer:

let the gradient of lines l,m,n be

m_{l},m_{m},m_{n}

then, according to question,

m_{l}=m_{m}

and

m_{n}m_{l}=-1

so,

m_{n}m_{m}=-1

so n is perpendicular to m

Answer 2

Step-by-step explanation:

Given: l, m, n are three lines such that l || m and n ⊥ l.

To prove: n ⊥ m

Proof :  

Since, n ⊥ l

→ ∠1 = 90° ………….(1)

Now,  l ‖ m and transversal intersects them.

∠2 = ∠1 ………(2)

Thus, the corresponding angles made by the transversal n with lines l and m are equal.

From eq (1) & (2) , we get ∠2 = ∠1 = 90°

→ ∠2  = 90°

Hence, n is perpendicular to m (n ⊥  m).

Figure of this answer is in the attachment below.

• Hope this help you !