This image displays a completed geometry worksheet that defines the fundamental concepts of points, lines, and planes with handwritten student notes.

Problem Analysis:

The image provided is a worksheet covering fundamental concepts in geometry, specifically focusing on points, lines, planes, and their intersections. The task involves filling in the blanks to complete the definitions and examples related to these geometric concepts.

Solution and Explanation:

#### 1. Point
- Definition: A point is a location.
- A point represents a specific position in space but has no size or shape.
- Properties:
- It has no size or shape.
- Always use a CAPITAL LETTER to name a point.
- Example: Point \( A \).

#### 2. Line
- Definition: A line is made up of points.
- A line is a one-dimensional figure that extends infinitely in both directions.
- Properties:
- Any 2 points form a line.
- A line has no thickness or width.
- Name a line by any two points on the line, or a lowercase script letter.
- Example:
- Using two points: \( \overleftrightarrow{XY} \), \( \text{line } n \), \( \text{line } xy \).
- Collinear Points: Points that lie on the same line.
- Non-Collinear Points: Points that do NOT lie on the same line. (Must be at least three points.)

#### 3. Plane
- Definition: A plane is a flat surface made up of points.
- A plane is a two-dimensional figure that extends indefinitely in all directions.
- Properties:
- Any 3 non-collinear points make up a plane.
- A plane extends indefinitely in all directions.
- Name a plane by any three non-collinear points on the plane, or an uppercase script letter.
- Example:
- Using three points: \( \text{plane } P \), \( \text{plane } KJL \).
- Coplanar Points: Points that lie on the same plane.
- Non-Coplanar Points: Points that do NOT lie on the same plane. (Must be at least four points.)

#### 4. Intersecting Lines & Planes
- Intersecting Lines: Two lines intersect at a point.
- When two lines cross each other, they meet at a single point.
- Intersecting Planes: Two planes intersect at a line.
- When two planes cross each other, they form a line where they meet.

Final Answers:

- Point: location, size, shape, CAPITAL LETTER, point \( A \)
- Line: points, 2, thickness, width, two, \( \overleftrightarrow{XY} \), line \( n \), line \( xy \), collinear points, non-collinear points
- Plane: flat surface, 3, three, plane \( P \), plane \( KJL \), coplanar points, non-coplanar points
- Intersecting Lines & Planes: point, line

Boxed Final Answer:

\[
\boxed{
\text{Point: location, size, shape, CAPITAL LETTER, point } A \\
\text{Line: points, 2, thickness, width, two, } \overleftrightarrow{XY}, \text{ line } n, \text{ line } xy, \text{ collinear points, non-collinear points} \\
\text{Plane: flat surface, 3, three, plane } P, \text{ plane } KJL, \text{ coplanar points, non-coplanar points} \\
\text{Intersecting Lines & Planes: point, line}
}
\]