Are the following 15 statements true or false 1 By definitio

Are the following 15 statements true or false?

1. By definition, a line m is \"parallel\" to a line l if for any two points P, Q on m, the perpendicular distance from P to l is the same as the perpendicular distance from Q to l.

2. It was unnecessary for Euclid to assume the parallel postulate because the French mathematician Legendre proved it.

3. A \"transversal\" to two lines is another line that intersects both of them in distict points.

4. \"Axioms\" or \"Postulates\" are statements that are assumed, without further justification, whereas \"theorems\" or \"propositions\" are proved using the axioms.

5. We call sqrt(2) an \"irrational number\" because it cannot be expressed as a quotient of two whole numbers.

6. The ancient Greeks were the first to insist on proofs for mathematical statements to make sure they were correct.

7. The precise technology of measurment availble to us today confirms the Pythagoreans\' claim that sqrt(2) is irrational

8. The ancient Greek astronomers did not believe that three-dimensional euclidean geometry was a idealized model of the entire space in which we live because they believed the universe is finite in extent, whereas Euclidean lines can be extended indefinitely.

Solution

1)T, explanation: perpendicular Distance between two parallel lines at any points are always equal.

2)F. , 3)T, by definition of transversal.

4)T, by definitions of axioms and postulates

5)F, irrational number can be expressed as ratio of two integers(not whole numbers) in the form of p/q (q#0) 6)T. , from the history it is clear 7) F. 8). T.