Table of Contents

- 1 Do any three points not on the same line determine a plane?
- 2 Are 3 points always on the same plane?
- 3 Can any three points be a plane?
- 4 What postulate that says through any two points there is exactly one line?
- 5 What is the intersection of 3 planes?
- 6 When do lines lie in more than one plane?
- 7 What happens when two lines in a plane are not parallel?

## Do any three points not on the same line determine a plane?

Three non-collinear points determine a plane. This statement means that if you have three points not on one line, then only one specific plane can go through those points. The plane is determined by the three points because the points show you exactly where the plane is.

**Is it true that through any three points there is exactly one line?**

Through any three non-collinear points, there exists exactly one plane. A plane contains at least three non-collinear points. If two points lie in a plane, then the line containing them lies in the plane. If two planes intersect, then their intersection is a line.

### Are 3 points always on the same plane?

For example, three points are always coplanar, and if the points are distinct and non-collinear, the plane they determine is unique. However, a set of four or more distinct points will, in general, not lie in a single plane. Two lines in three-dimensional space are coplanar if there is a plane that includes them both.

**Is the following statement true or false the intersection of three planes can be a line?**

Three planes can intersect at a point. Three planes can intersect at a line. parallel, then they must intersect. If lines are perpendicular to the same plane, they are parallel.

#### Can any three points be a plane?

In a three-dimensional space, a plane can be defined by three points it contains, as long as those points are not on the same line.

**What are 3 non collinear points?**

Points B, E, C and F do not lie on that line. Hence, these points A, B, C, D, E, F are called non – collinear points. If we join three non – collinear points L, M and N lie on the plane of paper, then we will get a closed figure bounded by three line segments LM, MN and NL.

## What postulate that says through any two points there is exactly one line?

Through any two points, there is exactly one line (Postulate 3). If two points lie in a plane, then the line joining them lies in that plane (Postulate 5). If two planes intersect, then their intersection is a line (Postulate 6).

**What is through any two points?**

through any two points, there is exactly one line. a line contains at least two points. If two planes intersect, then their intersection is a line.

### What is the intersection of 3 planes?

Each plan intersects at a point. 3. The second and third planes are coincident and the first is cuting them, therefore the three planes intersect in a line.

**Is the following statement true or false a plane extends forever?**

A plane is a flat surface that contains infinitely many intersecting lines that extend forever in all directions. Think of a plane as a huge sheet of paper with no thickness that goes on forever.

#### When do lines lie in more than one plane?

a line and a point, not on that line, lie in more than one plane never a line contains exactly one point never when a and b are in a plane, ab (arrow on top) is in that plane always if two points are collinear, then they are coplanar always

**Is the phrase ” exactly one ” true or false?**

– any two points are collinear true – a postulate is a statement assumed to be true without proof true – the phrase “exactly one” has the same meaning as the phrase “one and only one” true – three points determine a plane false – through any two points there is exactly one plane false

## What happens when two lines in a plane are not parallel?

Given two lines in the two-dimensional plane, the lines are equal, they are parallel but not equal, or they intersect in a single point. In three dimensions, a fourth case is possible. If two lines in space are not parallel, but do not intersect, then the lines are said to be skew lines ( (Figure) ).

**When are three points are coplanar then they are collinear?**

if three points are coplanar, then they are collinear sometimes if three points are noncollinear, then they are coplanar always three noncollinear points cannot lie in more than one plane always for any three points in space, more than one plane can contain them sometimes if two different planes intersect, then their intersection is a line