Geometry Worksheet 1.1 Name Points, Lines, and Planes Per __.pdf - Free Printable

Problem: Geometry Worksheet 1.1 - Points, Lines, and Planes

The worksheet involves identifying points, lines, and planes in various diagrams. Below is a detailed solution for each problem.

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Problem 1

#### Diagram:
A rectangular prism with labeled vertices \( A, B, C, D, E, F, G, H \).

#### Questions:
1. Name two coplanar lines:
- Coplanar lines lie in the same plane.
- Example: \( AB \) and \( AD \) (both lie in the bottom face of the prism).
- Another example: \( EF \) and \( EH \) (both lie in the top face of the prism).

2. Name four coplanar points:
- Coplanar points lie in the same plane.
- Example: \( A, B, C, D \) (all lie in the bottom face of the prism).
- Another example: \( E, F, G, H \) (all lie in the top face of the prism).

3. Name four non-coplanar points:
- Non-coplanar points do not lie in the same plane.
- Example: \( A, B, E, H \) (these points are at the corners of the prism and do not all lie in one plane).

4. Name plane \( R \) in four different ways:
- Plane \( R \) can be named using any three non-collinear points that lie in it.
- Example: Plane \( ABC \), Plane \( ABD \), Plane \( ACD \), Plane \( BCD \).

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Problem 2

#### Diagram:
A triangular prism with labeled vertices \( A, B, C, D, E, F, G, H, J, K \).

#### Questions:
1. How many planes are in the diagram?
- The triangular prism has two triangular bases and three rectangular lateral faces.
- Total planes: 5 (two triangular bases + three rectangular faces).

2. Name all of the planes:
- Plane \( ABG \) (triangular base).
- Plane \( CDH \) (triangular base).
- Plane \( AGH \) (rectangular face).
- Plane \( BCG \) (rectangular face).
- Plane \( BDH \) (rectangular face).

3. Name three collinear points:
- Collinear points lie on the same line.
- Example: \( A, G, H \) (all lie on the edge \( AH \)).
- Another example: \( B, C, G \) (all lie on the edge \( BG \)).

4. Name three non-collinear points:
- Non-collinear points do not lie on the same line.
- Example: \( A, B, G \) (these points form a triangle).

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Problem 3

#### Diagram:
A rectangular prism with labeled vertices \( P, Q, R, S, T, U, V, W \) and additional lines \( m \) and \( n \).

#### Questions:
1. Name the line with point \( P \) in 4 different ways:
- Line \( PQ \), Line \( PR \), Line \( PS \), Line \( PW \).

2. Name the line with point \( T \) in 3 different ways:
- Line \( TU \), Line \( TV \), Line \( TW \).

3. Name the plane in 4 different ways:
- Plane \( PQRS \), Plane \( PQWT \), Plane \( QRST \), Plane \( RSTU \).

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Problem 4

#### Diagram:
A triangular pyramid (tetrahedron) with labeled vertices \( A, B, C, D, E \) and plane \( N \).

#### Questions:
1. How many planes are in the diagram?
- The tetrahedron has 4 triangular faces.
- Total planes: 4.

2. Is plane \( N \) the same as plane \( ABC \)?
- Yes, plane \( N \) is the same as plane \( ABC \) because they both refer to the same triangular face.

3. Name three collinear points:
- Example: \( A, B, C \) (all lie on the base of the tetrahedron).

4. Name three non-collinear points:
- Example: \( A, B, D \) (these points form a triangular face).

5. Name two intersecting lines and their point of intersection:
- Example: Line \( AB \) and Line \( AC \) intersect at point \( A \).

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Problem 5

#### Diagram:
A parallelogram with labeled vertices \( P, Q, R, S \) and additional lines \( m \) and \( n \).

#### Questions:
1. Name the line in four different ways:
- Line \( PQ \), Line \( QR \), Line \( RS \), Line \( SP \).

2. Name the plane in four different ways:
- Plane \( PQRS \), Plane \( PQm \), Plane \( QRn \), Plane \( RSQ \).

3. Name 3 non-collinear points:
- Example: \( P, Q, R \) (these points form a triangle).

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Problem 6

#### Diagram:
A complex 3D figure with multiple intersecting planes and labeled points \( A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P \).

#### Questions:
1. Are points \( A, B, D \) coplanar?
- Yes, points \( A, B, D \) lie in the same plane (the front face of the figure).

2. Name all of the planes in the diagram:
- Plane \( ABCD \), Plane \( AEFG \), Plane \( BHJK \), Plane \( DLMP \), Plane \( INOQ \).

3. What is at the intersection of the three planes?
- The intersection of three planes is typically a point where they meet.
- Example: Point \( A \) is the intersection of planes \( ABCD \), \( AEFG \), and \( BHJK \).

4. Name the intersection of the three planes:
- Intersection: Point \( A \).

5. Name four non-coplanar points:
- Example: \( A, E, H, L \) (these points do not all lie in the same plane).

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Final Answer

\[
\boxed{
\text{See detailed solutions above for each problem.}
}
\]