Are Points That Lie on the Same Plane?

Definition of Coplanar, Collinear, and Non-Collinear Points

• Points lying on the same plane are coplanar points.
• Two intersecting lines in a plane are coplanar.
• Three non-collinear points determine a unique plane.
• Non-coplanar lines intersect at a point.
• Coplanar lines may be parallel or intersect at a point.
• Intersecting lines are coplanar.

Coplanar Lines and Collinear Points in Geometry

• In a plane, two intersecting lines are coplanar.
• Three non-collinear points define a plane.
• Four coplanar points define either a plane or a line containing three of them.
• Non-coplanar points generate vectors not confined to any one plane.
• Coplanar points generate vectors lying in their plane.

Examples and Explanations

• The hands of an analog clock always lie and move on the same background plane.
• Paint drops on a canvas are examples of coplanar points.
• Non-coplanar lines are non-intersecting and not satisfying the vector determinant condition.

Explanation on Line and Coplanar Points

• Points or lines are said to be coplanar if they lie in the same plane.
• Two angles with the same measure are congruent angles.
• A plane can be defined by three non-collinear points in three-dimensional space.
• Points and lines in the same plane are coplanar.

Additional Information

• Understanding the relationships between points, lines, and planes is crucial in geometry.
• Review these foundational concepts frequently to strengthen your knowledge.
• If four points are on the same plane, any fourth point will determine a plane they all lie on.