Worksheet: Points, Lines, and Planes - Collinear and Coplanar ... - Free Printable

It looks like you've uploaded a worksheet titled "Points, Lines, and Planes" from Kuta Software, which contains geometry problems involving points, lines, planes, and their relationships in space. Since I can't view images directly, I’ll help you solve the problems based on the text content you’ve provided.

Let’s go through each problem step by step.

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Problem 1: Name the two planes in the figure.

From typical diagrams in such worksheets (especially with labeled points and intersecting planes), the figure likely shows two intersecting planes, often labeled with three non-collinear points.

Assuming the diagram includes:

- Points A, B, C, D, E, F, G, H (common in cube-like figures)
- Two planes: one might be plane ABC, another plane ABD or similar

But since the exact labels aren’t visible, here's how to approach it:

> Answer:
> If the figure shows a rectangular prism or cube, the two planes are typically:
> - Plane ABCD
> - Plane EFGH
> or
> - Plane ABFE
> - Plane BCGF

But without seeing the image, the safest assumption is that the two planes are named using three non-collinear points on each.

So, example answer:
> Plane ABC and Plane ADE

*(Note: Replace with actual labels from your diagram.)*

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Problem 2: List the points labeled in the figure.

This asks for all the labeled points in the diagram.

Commonly, these are letters like A, B, C, D, E, F, G, H — depending on the figure.

> Example Answer:
> A, B, C, D, E, F, G, H

*(Again, adjust based on your diagram.)*

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Problem 3: Classify each statement as true or false.

We'll analyze each one logically.

#### (1) $\overline{AB}$ contains A

- $\overline{AB}$ is a line segment between A and B.
- It includes both endpoints A and B.
- ✔ True

#### (2) $\overline{AB}$ contains B

- Same reason as above.
- ✔ True

#### (3) Plane S contains AB and CD

- This depends on whether points A, B, C, D lie on plane S.
- But if AB and CD are not coplanar, this would be false.
- Without a diagram, assume that AB and CD are on the same plane.
- However, if they’re skew lines, then no single plane contains both.
- But since the question says "plane S", and assumes it exists, we must check if both segments lie on it.

If AB and CD are in the same plane (e.g., both in plane ABCD), then:
- ✔ True

But if they're not, then:
- ✘ False

> Assumption: Based on standard diagrams, AB and CD may be in the same plane.

➡️ Answer: True

#### (4) $\overrightarrow{AB}$ contains B

- $\overrightarrow{AB}$ is a ray starting at A and going through B.
- It includes point B.
- ✔ True

#### (5) A and C determine a line

- Any two distinct points determine a unique line.
- So, A and C define line AC.
- ✔ True

#### (6) C, D, A, and F are coplanar

- Four points are coplanar if they lie in the same plane.
- If C, D, A, F are on the same face of a cube, yes.
- But if F is not on the same plane as A, C, D, then no.

In many diagrams:
- A, C, D are on the bottom face.
- F is on the top face → not coplanar with A, C, D.

So unless specified otherwise, likely:
- ✘ False

> Answer: False

#### (7) A, B, and C are collinear

- Collinear means all three lie on the same straight line.
- But A, B, C are usually vertices of a triangle or rectangle → not on a line.
- So unless they're on a straight edge, they are not collinear.

➡️ Answer: False

#### (8) $\overline{AB}$ contains A and B

- Segment AB includes both endpoints.
- ✔ True

#### (9) A and C are collinear

- Two points are always collinear — any two points define a line.
- So yes, A and C are collinear.

➡️ Answer: True

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Final Answers Summary:

| Statement | Answer |
|---------|--------|
| (1) $\overline{AB}$ contains A | True |
| (2) $\overline{AB}$ contains B | True |
| (3) Plane S contains AB and CD | True *(if AB and CD lie on plane S)* |
| (4) $\overrightarrow{AB}$ contains B | True |
| (5) A and C determine a line | True |
| (6) C, D, A, and F are coplanar | False |
| (7) A, B, and C are collinear | False |
| (8) $\overline{AB}$ contains A and B | True |
| (9) A and C are collinear | True |

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Notes:

- The answers depend heavily on the diagram. For example:
- If AB and CD are skew lines, (3) is false.
- If A, B, C are on a straight line, (7) is true.
- In most textbook diagrams (like cubes), A, B, C are corners of a face — not collinear.
- Points A, C, D, F are usually not coplanar if F is on the opposite side.

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Recommendation:

If you can describe the diagram (e.g., “it’s a cube with points A, B, C, D on the bottom face and E, F, G, H on the top”), I can give more accurate answers.

For now, here’s a final answer key assuming a standard cube diagram:

> 1. Plane ABC and Plane EFG
> 2. A, B, C, D, E, F, G, H
> 3.
> (1) True
> (2) True
> (3) True
> (4) True
> (5) True
> (6) False
> (7) False
> (8) True
> (9) True

Let me know if you’d like this formatted for printing or if you can describe the diagram further!