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

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Solution

The figure can be drawn as follows:

Here, and

We need to prove that .

It is given that, therefore,

(i)

We have, thus,and are the corresponding angles. Therefore,these must be equal. That is,

From equation (i), we get:

Therefore,.

Hence proved.

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

The figure can be drawn as follows: Here, and We need to prove that . It is given that, therefore, (i) We have, thus,and are the corresponding angles. Therefore,these must be equal. That is, From equation (i), we get: Therefore,. Hence proved.

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

The figure can be drawn as follows:

Here, and

We need to prove that .

It is given that, therefore,

(i)

We have, thus,and are the corresponding angles. Therefore,these must be equal. That is,

From equation (i), we get:

Therefore,.

Hence proved.