Study the following statement: “Two intersecting lines cannot be perpendicular to the same line”. Check whether it is an equivalent version to the Euclid’s fifth postulate. [Hint : Identify the two intersecting lines l and m and the line n in the above statement.]
Solution:
Given, the statement is “Two intersecting lines cannot be perpendicular to the same line”.
We have to determine an equivalent version to the Euclid’s fifth postulate.
Euclid’s fifth postulate states that if a straight line falling on two straight lines makes the interior angles on the same side of it, taken together less than two right angles, then the the two straight lines if produced indefinitely, meet on that side on which the sum of angles is taken together
less than two right angles.
Two equivalent version to the Euclid’s fifth postulate are
1) For every line l and for every point P not lying on Z, there exists a unique line m passing through P and parallel to Z.
2) Two distinct intersecting lines cannot be parallel to the same line.
Therefore, the given statement is not an equivalent version to Euclid's fifth postulate.
✦ Try This: In the given diagram light is travelling through different media. It is noted by a scientist that ∠1= ∠3= ∠4 but ∠2 <∠1. State whether the following statement is true or false. “Medium 1 is the denser than medium 3 but it’s density is equal to medium 2”
☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 5
NCERT Exemplar Class 9 Maths Exercise 5.4 Problem 2
Study the following statement: “Two intersecting lines cannot be perpendicular to the same line”. Check whether it is an equivalent version to the Euclid’s fifth postulate. [Hint : Identify the two intersecting lines l and m and the line n in the above statement
Summary:
For the following statement, “Two intersecting lines cannot be perpendicular to the same line”. It is not an equivalent version to Euclid's fifth postulate
☛ Related Questions:
- Read the following statements which are taken as axioms : (i) If a transversal intersects two parall . . . .
- Read the following two statements which are taken as axioms: (i) If two lines intersect each other, . . . .
- Read the following axioms: (i) Things which are equal to the same thing are equal to one another, (i . . . .