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.

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Solution

Two equivalent versions of Euclid’s fifth postulate are:
$(1)$ For every line $l$ and for every point $P$ not lying on $l$ , there exists a unique line $m$ passing through $P$ and parallel to $l$ .
$(2)$ Two distinct intersecting lines cannot be parallel to the same line.
From above two statements it is clear that, given statement is not an equivalent version to the Euclid’s fifth postulate.
Hence, “Two intersecting lines cannot be perpendicular to the same line” is not an equivalent version to the Euclid’s fifth postulate.

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Similar questions

Q. State which of the following statements are true (T) or which are false (F):

(i) If two lines in the same plane do not interest, then they much be parallel.
(ii) Distance between two parallel lines is not same every where.
(iii) If m ⊥ i, n ⊥ i and m ≠ n, then m ∥ n.
(iv) Two non-intersection coplanar rays are parallel.
(v) If ray AB ∥ line , then line segment AB ∥ m.
(vi) If line AB ∥ line , then line segment AB ∥ m.
(vii) No two parallel segments intersect.
(viii) Every pair of lines is a pair of coplanar lines.
(ix) Two lines perpendicular to the same line are parallel.
(x) A line perpendicular to one of two parallel lines is perpendicular to the other.

Which of the following statements are true (I) and which are false (F)? Give reasons.
(i) If two lines are intersected by a transversal, then corresponding angles are equal.
(ii) If two parallel lines are intersected by a transversal, then alternate interior angles are equal.
(iii) Two lines perpendicular to the same line are perpendicular to each other.
(iv) Two lines parallel to the same line are parallel to each other.
(v) If two parallel lines are intersected by a transversal, then the interior angles on the same side of the transversal are equal.

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.]

Write two equivalent versions of Euclid's fifth postulate

Q. Write the equivalent version of Euclid's fifth postulate.

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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.

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.