Worksheet for practicing naming points, lines, and planes with diagrams and handwritten answers.

Problem Analysis and Solution

The worksheet focuses on naming points, lines, and planes based on given diagrams. Below is a detailed explanation of each problem and its solution.

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#### Problem 1: Use the diagram to name the following.

Diagram:
- Points: \( H, N, K, I, M, O, L, J \)
- Lines: \( p, q, r \)

##### a) Four collinear points.
- Collinear points are points that lie on the same line.
- From the diagram, points \( H, N, K, I \) all lie on line \( r \).
- Answer: \( H, N, K, I \)

##### b) A line that contains point \( M \).
- Point \( M \) lies on line \( p \).
- Answer: Line \( p \)

##### c) A line that contains points \( H \) and \( K \).
- Points \( H \) and \( K \) both lie on line \( r \).
- Answer: Line \( r \)

##### d) Another name for line \( q \).
- Line \( q \) can also be named using any two points on it. For example, \( JL \), \( LJ \), or \( KL \).
- Answer: \( JL, LJ, KL \)

##### e) The intersection of lines \( p \) and \( r \).
- The intersection of two lines is the point where they meet.
- Lines \( p \) and \( r \) intersect at point \( N \).
- Answer: \( N \)

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#### Problem 2: Use the diagram to name the following.

Diagram:
- Points: \( A, B, C, D, E, F, M \)
- Lines: \( j, k \)
- Plane: \( M \)

##### a) A line containing point \( F \).
- Point \( F \) lies on line \( k \).
- Answer: Line \( k \)

##### b) Another name for line \( k \).
- Line \( k \) can also be named using any two points on it. For example, \( BE \), \( BC \), or \( EC \).
- Answer: \( BE, BC, EC \)

##### c) A plane containing point \( A \).
- Point \( A \) lies in plane \( M \).
- Answer: Plane \( M \)

##### d) An example of three non-collinear points.
- Non-collinear points are points that do not lie on the same line.
- Points \( A, B, D \) are non-collinear.
- Answer: \( A, B, D \)

##### e) The intersection of plane \( M \) and line \( k \).
- The intersection of a plane and a line is the point where the line crosses the plane.
- Line \( k \) intersects plane \( M \) at point \( E \).
- Answer: \( E \)

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#### Problem 3: Use the diagram to name the following.

Diagram:
- Points: \( X, Y, Z, W, T \)
- Planes: \( P, Q, R, S, T \)

##### a) Three coplanar points.
- Coplanar points are points that lie in the same plane.
- Points \( X, Y, Z \) all lie in plane \( P \).
- Answer: \( X, Y, Z \)

##### b) A plane containing point \( X \).
- Point \( X \) lies in plane \( P \).
- Answer: Plane \( P \)

##### c) The intersection of plane \( P \) and plane \( Q \).
- The intersection of two planes is a line.
- Planes \( P \) and \( Q \) intersect along line \( XY \).
- Answer: Line \( XY \)

##### d) How many planes are shown in the figure?
- The diagram shows five planes labeled \( P, Q, R, S, T \).
- Answer: 5

##### e) How many planes contain point \( X \)?
- Point \( X \) lies in planes \( P, Q, \) and \( R \).
- Answer: 3

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#### Problem 4: Use the diagram to name the following.

Diagram:
- Points: \( A, B, C, D, E, F \)
- Lines: \( l, m, n \)
- Planes: \( P, Q, R \)

##### a) The intersection of lines \( l \) and \( m \).
- The intersection of two lines is the point where they meet.
- Lines \( l \) and \( m \) intersect at point \( E \).
- Answer: \( E \)

##### b) Another name for plane \( Q \).
- Plane \( Q \) can also be named using any three non-collinear points on it. For example, \( ABC \) or \( ABE \).
- Answer: \( ABC, ABE \)

##### c) A point that lies on both planes \( P \) and \( Q \).
- Points that lie on both planes \( P \) and \( Q \) are points of intersection between the planes.
- Point \( D \) lies on both planes \( P \) and \( Q \).
- Answer: \( D \)

##### d) How many lines do planes \( P \) and \( Q \) intersect?
- The intersection of two planes is a single line.
- Planes \( P \) and \( Q \) intersect along line \( AD \).
- Answer: 1

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Final Answers:

1.
- a) \( H, N, K, I \)
- b) Line \( p \)
- c) Line \( r \)
- d) \( JL, LJ, KL \)
- e) \( N \)

2.
- a) Line \( k \)
- b) \( BE, BC, EC \)
- c) Plane \( M \)
- d) \( A, B, D \)
- e) \( E \)

3.
- a) \( X, Y, Z \)
- b) Plane \( P \)
- c) Line \( XY \)
- d) 5
- e) 3

4.
- a) \( E \)
- b) \( ABC, ABE \)
- c) \( D \)
- d) 1

Final Boxed Answers:
\[
\boxed{
\begin{array}{l}
1. \text{a) } H, N, K, I \\
\text{b) Line } p \\
\text{c) Line } r \\
\text{d) } JL, LJ, KL \\
\text{e) } N \\
2. \text{a) Line } k \\
\text{b) } BE, BC, EC \\
\text{c) Plane } M \\
\text{d) } A, B, D \\
\text{e) } E \\
3. \text{a) } X, Y, Z \\
\text{b) Plane } P \\
\text{c) Line } XY \\
\text{d) 5} \\
\text{e) 3} \\
4. \text{a) } E \\
\text{b) } ABC, ABE \\
\text{c) } D \\
\text{d) 1} \\
\end{array}
}
\]