Question

Lara wrote the statements shown in the chart below: Statement Description 1 If two lines intersect, then they intersect at exactly one point. 2 In a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the length of the legs. Which option best classifies Lara's statements?

Answer 1

This question comes with these four statements as answer choices:

Statement 1 and Statement 2 are postulates because they are true facts.
Statement 1 is a theorem, and Statement 2 is a postulate.
Statement 1 and Statement 2 are theorems because they can be proved.
Statement 1 is a postulate, and Statement 2 is a theorem.

Answer: the third choice, "Statement 1 and Statement 2 are theorems because they can be proved."

Justification:


To answer this question you must rely in the definitions of the terms postulate and theorem.

1) Postulate: it is a statement that is assumed to be true, without proove. The theorems rely on postulates.

2) Theorem: it is an important mathematical result that can be proved from one or more posutalates.

So, the difference is that postulates are considered true without being proved, and theorems have to be proved.

3) The statement 1, if two lines intersect, then they intersect at exactly one point, can be proved either algebraically or geometrically, so it is a theorem.


4) The statement 2, in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the length of the legs. This is the famous theorem of Pytagoras, for right triangles. It has been proved in many ways, mainly using the geometric arguments using areas, but also in other ways.


So, from point 3 and 4, the two statements are theorems.