Question

If, l, m, n are three lines such that l||m and n⊥ l, prove that n⊥ m.

Answer 1

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 ANSWER WILL HELP YOU…..

Similar questions :

In the given figure, find the values of x and y and then show that AB || CD.

https://brainly.in/question/1392122

 

In the given figure, if AB || CD, CD || EF and y: z = 3: 7, find x.

https://brainly.in/question/1392125

Answer 2

Given:

l || m and n⊥ l

To prove:

n⊥ m

Proof:

If l || m, and n⊥ l:

Angle formed by n on l will be equal to 90°

And when l || m, corresponding angles are equal. Thus:

Angle formed by n on m will also be equal to 90°

Therefore, n⊥ m.

Hence Proved.