Question

Abigail wrote the statements shown in the chart. . Statement. Description. . 1. If two lines intersect, then exactly one plane contains both lines.. . 2. If a point lies outside a line, then exactly one plane contains both the line and the point.. . . Which option best classifies Abigail’s statements? . A) Statement 1 and Statement 2 are postulates because they are true facts. B) Statement 1 and Statement 2 are theorems because they can be proved with the help of appropriate postulates. C) Statement 1 is a theorem because it can be proved and Statement 2 is a postulate because it can be proved

Answer 1

Out of the choices given, the option that best classifies Abigail's statements is they are both theorems because they can be proved with the help of appropriate postulates. The correct answer is B. 

Answer 2

The correct answer is:

B) Statement 1 and Statement 2 are theorems because they can be proved with the help of appropriate postulates.

Explanation:

Statement 1 is the Line Intersection Theorem. To prove this, we use postulates about having only one plane passing through any 3 noncollinear points. We would choose two points from one line and one point from the second; they would be non-collinear points and be in one plane. This also works choosing the points the opposite way.

Statement 2 is the Point and Line Contained in Plane Theorem. Again, if two lines intersect, we can choose three points to define a plane. We have to prove that both lines are in the plane. We rely on previously proven postulates to do this.