Question

Prove that two lines that are respectively parallel to
two intersecting lines intersect each other.

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Answer 1

⚡ Given⚡

Let lines l and m are two intersecting lines. Again, let n and p be another two lines which are perpendicular to the intersecting lines meet at point D.

⚡To prove⚡

Two lines n and p intersecting at a point.

⚡Proof ⚡

Suppose we consider lines n and p are not intersecting, then it means they are parallel to each other i.e., n || p …(i)

Since, lines n and pare perpendicular to m and l, respectively.

But from Eq. (i) n || p it implies that l || m.

Hence, it is a contradiction.

Thus, our assumption is wrong.

Therefore, lines n and p intersect at a point.

Answer 2

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