Prove that two lines that are respectively perpendicular to two intersecting lines intersect each other by proof of contradiction

Solution:

Consider two intersecting line l and m

Let n and p be another two lines intersecting at the point D

We have to prove that n and p are perpendicular to the intersecting lines m and l.

considering lines n and p do not intersect,

This implies the lines are parallel to each other

So, n || p ------------------------- (1)

Given, lines n and p are perpendicular to m and l

From equation (1), we get

l || m

This implies the assumed statement is a contradiction.

So, the assumption that the lines n and p do not intersect is wrong.

Therefore, lines n and p intersect at a point.

✦ Try This: In the given figure, p∥q and r∥s. Find the values of x,y and z.

☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 6

NCERT Exemplar Class 9 Maths Exercise 6.4 Problem 5

Prove that two lines that are respectively perpendicular to two intersecting lines intersect each other by proof of contradiction

Summary:

Proof by contradiction is a form of proof that establishes the truth or the validity of a proposition, by showing that assuming the proposition to be false leads to a contradiction. It is proven that two lines that are respectively perpendicular to two intersecting lines intersect each other by proof of contradiction

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