1. The statement a line and a point not on the line lie in exactly one plane. is true.
2. The postulates states that a quantity must be equal to itself is reflexive
3. The statement if two planes intersect they form a line is always true.
4. The axiom would justify the following conclusion is subtraction.
1. A-line and a point not on the line lie in exactly one plane.
What is a point?
A point is a location in space which has no length, width , or height.
What is a line?
A line is a one dimensional figure that has length but no width
What is a plane?
A plane is a flat surface that contains 3 or more points.
Since a plane passes through 3 points and a line contains two points, then the point not on the line contains the third point on the plane. That is, they are not collinear.
So, a line and a point not on the line lie in exactly one plane.
So, the statement a line and a point not on the line lie in exactly one plane. is true.
2. Which of the following postulates states that a quantity must be equal to itself?
For a quantity to be equal to itself, it is said to be reflexive
So, the postulates states that a quantity must be equal to itself is reflexive
3. If two planes intersect they form a line.
Since a plane contains 3 or more points and a line contains two points, when two planes intersect, they contain at least two points and thus form a line.
So, the statement if two planes intersect they form a line is always true.
4. Which axiom would justify the following conclusion?
If x + 4 = 12, then x = 8.
Since x + 4 = 12
Subtracting 4 from both sides, we have
x + 4 - 4 = 12 - 4
x = 8
So, the axiom would justify the following conclusion is subtraction.
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