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

It looks like you've uploaded a geometry worksheet with several problems related to points, lines, planes, and their relationships in space (especially 3D geometry). Since I can't view images directly, I’ll solve the problems based on the text you provided. Let's go through each question step by step.

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Question 7:

*Diagram shows a cube or rectangular prism with labeled points A, B, C, D, E, F, G, H.*

a. Are points A, C, and E coplanar?

- Points A, C, and E are three vertices of the cube.
- In a cube, any three points are generally coplanar unless they form a "skew" configuration.
- But A, C, and E are not necessarily on the same face. For example:
- If A is bottom front left,
- C is bottom back right,
- E is top front right,
- Then these three points may lie on different faces.
- However, any three points are always coplanar, because three non-collinear points define a plane.

✔ Answer: Yes, points A, C, and E are coplanar. (Any three points are coplanar.)

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b. Name the three lines:

We need to identify three lines in the diagram. Common lines would be edges of the cube.

Examples:
- Line AB
- Line AD
- Line AE

But since it’s not specified, let’s assume standard labeling:

Let’s suppose:
- A, B, C, D are bottom face (clockwise)
- E, F, G, H are top face (E above A, etc.)

Then possible lines:
- AB, AC, AE (or any three distinct edges)

✔ Answer: Example: AB, AD, AE

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c. Name three collinear points:

Collinear means lying on the same straight line.

In a cube, no three vertices are collinear — all corners are at right angles.

So no three vertices of a cube are collinear.

But wait — if there’s a diagonal or edge, maybe?

Actually, only two points define a line segment between vertices.

So there are no three collinear vertices in a cube.

But perhaps the diagram includes diagonals or extended lines?

Wait — maybe the problem allows for points along an edge?

For example:
If point M is midpoint of AB, then A, M, B are collinear.

But from the way it's written, likely only labeled points.

Since only A, B, C, D, E, F, G, H are labeled, and no midpoints, no three labeled points are collinear.

But this seems odd.

Wait — perhaps the diagram has a diagonal?

Alternatively, maybe A, B, C are not collinear — but what about A, B, F? No.

Actually, in a cube, no three vertices are collinear.

So unless there's a typo or additional points, there are no three collinear points among the vertices.

But perhaps the problem expects something like:

- A, B, C — but they’re not collinear.

Wait — maybe the diagram isn’t a cube? Or maybe it’s a different shape?

Given ambiguity, let’s assume the standard cube.

✔ Answer: There are no three collinear points among the vertices. But if we must name, perhaps A, B, and a midpoint — but not labeled.

Alternatively, maybe the diagram includes a line with multiple points?

Wait — perhaps A, C, and G? No — not collinear.

Let’s skip and come back.

Wait — maybe the diagram is a triangular prism or something else?

Looking at Question 9, it mentions W, X, Y, Z and a triangular base, so maybe Q7 is a cube.

But still — in a cube, no three vertices are collinear.

So unless there’s a typo, this part might have no answer.

But perhaps the question allows for points on a line, even if not vertices.

Alternatively, maybe A, B, and C are meant to be on a line? But that’s not true.

Wait — perhaps the diagram shows a line with points A, B, C — but in a cube, that’s not possible.

Maybe it’s not a cube?

Alternatively, perhaps A, C, and G are on a diagonal? But not collinear — they're not on the same straight line.

Wait — A, C, and G: A to C is diagonal on bottom, C to G is vertical, so not collinear.

Only three points are collinear if they lie on the same edge.

But each edge has only two vertices.

So no three labeled vertices are collinear.

So answer: None — but that can't be.

Wait — perhaps the diagram has four points on a line?

Unlikely.

Perhaps the problem assumes points are on a line, like in a net?

No.

Wait — maybe A, B, C are on a face, but not collinear.

I think there’s a mistake in interpretation.

Wait — maybe the diagram is not a cube, but a pyramid or something?

But Q7 has arrows, suggesting 3D.

Alternatively, perhaps A, B, C are on a straight line? Unlikely.

Wait — maybe the diagram shows points A, C, E on a diagonal?

But still, not collinear.

Let’s move to Q8 and see.

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Question 8:

*Cube diagram with points A, B, C, D, E, F, G, H*

a. How many planes are in the diagram?

A cube has 6 faces, each a plane.

Also, there are diagonal planes — but usually, in such problems, only faces are counted as planes unless otherwise stated.

So:

- Bottom: ABCD
- Top: EFGH
- Front: ABFE
- Back: CDHG
- Left: ADHE
- Right: BCGF

That’s 6 planes.

✔ Answer: 6 planes

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b. Name the planes:

- Plane ABCD (bottom)
- Plane EFGH (top)
- Plane ABFE (front)
- Plane CDHG (back)
- Plane ADHE (left)
- Plane BCGF (right)

✔ Answer: ABCD, EFGH, ABFE, CDHG, ADHE, BCGF

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c. Name six coplanar points:

Six points on one plane.

For example, on the bottom face: A, B, C, D, and say, if there are midpoints, but only vertices.

But only four vertices per face.

So maximum four points per face.

So cannot have six coplanar points among vertices.

But perhaps all eight vertices are coplanar? No — they are not.

So no six coplanar points.

Wait — but each face has four coplanar points.

So maximum four.

But the question asks for six coplanar points.

This suggests either:
- The diagram has more points (like midpoints), or
- It's a different figure.

But in a cube, only 8 vertices.

So impossible to have six coplanar vertices.

Unless the problem considers points on edges.

But only labeled points are given.

So probably, the intended answer is four.

But it says “six”.

Wait — maybe the entire cube is considered, and points are not just vertices?

But the diagram likely only labels vertices.

So this is problematic.

Wait — perhaps the question means “name six points that are coplanar”, not necessarily on one plane.

But that doesn’t make sense.

Wait — maybe it’s asking for six points that are coplanar, meaning on the same plane.

But again, only four per face.

So unless the plane is diagonal, like a space diagonal plane.

For example, plane ACEG — but that’s not a face.

But in a cube, there are diagonal planes that contain 4 points.

For example, the plane containing A, C, F, H — but not necessarily.

Wait — in a cube, a diagonal plane can contain four vertices.

Still not six.

So impossible.

Therefore, likely the question means: name four coplanar points, but it says “six”.

Wait — perhaps the diagram includes more than just vertices?

Or perhaps it’s not a cube, but a prism with more points?

Alternatively, maybe “six” is a typo.

But let’s look at Q9.

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Question 9:

*Diagram shows a triangular prism with points W, X, Y, Z, A, B, C, D*

From description:
- Base: triangle WXY
- Top: triangle ABC
- Edges: WA, XB, YC
- Also, point D on side BC? Or elsewhere?

Wait — it says: “Point B on $\overline{YZ}$” — but that contradicts.

Wait — the text says:

> 10. Point B on $\overline{YZ}$

But in Q9, it's a prism.

Let’s parse:

Q9: Diagram shows a prism with:
- W, X, Y on base
- A, B, C on top
- WA, XB, YC are lateral edges

Then:
- Point D is on BC?
- And angle at B is 90°?

And it says:
> 10. Point B on $\overline{YZ}$

But Z is not defined.

Wait — maybe it's a typo.

Wait — the text says:

> 9. [Diagram]
> a. Name six coplanar points:
> b. Name four non-coplanar points:
> c. How many planes are in the diagram?
> d. Name three collinear points:
> e. Are planes W and ABC different planes?

But then:

> 10. Point B on $\overline{YZ}$

Wait — maybe Z is a point?

But in Q9, only W, X, Y, A, B, C, D are mentioned.

Wait — perhaps the diagram has a point Z?

But not listed.

Alternatively, maybe it's a typo.

Wait — perhaps Z is the same as C? Unlikely.

Wait — maybe the diagram has a quadrilateral?

Alternatively, let’s ignore the confusion and focus on Q9.

Assume it’s a triangular prism with:
- Base: triangle WXY
- Top: triangle ABC
- Lateral edges: WA, XB, YC

Then:

a. Name six coplanar points:

Each face is a plane.

For example, the base face: W, X, Y — only three points.

The top face: A, B, C — three points.

Lateral faces:
- W, X, B, A — quadrilateral WABX
- X, Y, C, B — quadrilateral XBCY
- Y, W, A, C — quadrilateral YWAC

So each lateral face has four points.

So we can pick four coplanar points.

But question asks for six coplanar points.

Again, impossible unless more points.

But if the prism has only 6 vertices, maximum 4 per face.

So cannot have six coplanar points.

Unless the question means name six points that are coplanar — but again, not possible.

Wait — perhaps the entire set is coplanar? No.

So likely, the question means name four coplanar points.

But it says “six”.

Alternatively, maybe the diagram includes midpoints?

But not labeled.

So probably a typo.

Let’s assume it’s four.

But let’s look at Q10:

> 10. Point B on $\overline{YZ}$

This suggests that Y and Z are endpoints, and B is on segment YZ.

But in a prism, if Y is a base vertex, and Z is another point, perhaps Z is a top vertex?

But in Q9, top is A, B, C.

So if B is on YZ, then Z must be a point such that YZ contains B.

But B is a top vertex.

So unless Z is C or A, but then YZ would be a diagonal.

But if Y and Z are connected, and B lies on it, then B is on YZ.

But in a prism, B is not on any edge from Y unless it’s a diagonal.

So unlikely.

Perhaps Z is a point on the extension?

But not likely.

Alternatively, maybe the diagram is a pyramid?

Wait — Q9 shows a prism with triangular base.

But then Q10 says “Point B on $\overline{YZ}$”, which suggests that B is on a line segment between Y and Z.

So unless Z is a point such that YZ passes through B, but in a prism, B is not on any such segment.

So contradiction.

Wait — perhaps the diagram has a different structure.

Alternatively, maybe B is on YZ, and Y and Z are points on the base.

But then B is on the base, but in a prism, B is top.

So confusing.

Perhaps the labeling is off.

Let’s move to Q11–14, which are general definitions.

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Question 11:

> Plane J containing line s.

This is a statement, not a question.

But it’s likely a definition.

So: A plane contains a line if the line lies entirely within the plane.

So if line s is in plane J, then every point on s is in J.

✔ Answer: Plane J contains line s means that every point on line s lies in plane J.

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Question 12:

> Lines r and t intersect at pt Z.

This means: Lines r and t meet at a single point, Z.

So they are intersecting lines, and Z is their point of intersection.

✔ Answer: Lines r and t cross at point Z.

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Question 13:

> $\overrightarrow{JK}$ intersects $\overrightarrow{CD}$, with point Y not on either line.

- $\overrightarrow{JK}$ is a ray starting at J, going through K.
- $\overrightarrow{CD}$ is a ray starting at C, going through D.
- They intersect at some point (not named).
- Point Y is not on either ray.

So the rays cross at a point, and Y is somewhere else.

No specific answer needed — just understanding.

✔ Answer: The two rays cross at a point; Y is not on either ray.

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Question 14:

> Lines M and N intersect at $\overline{JJ}$

Wait — $\overline{JJ}$ is a line segment from J to J — which is a point.

So $\overline{JJ}$ is just point J.

So lines M and N intersect at point J.

✔ Answer: Lines M and N intersect at point J.

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Now back to earlier questions.

Let’s try to resolve Q7–9 with better assumptions.

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Revisiting Question 7:

Assume it’s a cube with vertices A, B, C, D, E, F, G, H.

Standard labeling:
- Bottom: A (front-left), B (front-right), C (back-right), D (back-left)
- Top: E (above A), F (above B), G (above C), H (above D)

Then:

a. Are points A, C, and E coplanar?

- A, C, E: A and C are diagonal on bottom, E is above A.
- These three points define a plane.
- Any three points are coplanar.

✔ Yes

b. Name the three lines:

- AB, AD, AE (edges from A)

✔ Answer: AB, AD, AE

c. Name three collinear points:

As before, no three vertices are collinear.

But perhaps the diagram includes a diagonal?

Wait — if it’s a net or something, but unlikely.

Alternatively, maybe A, B, C are on a line? No.

Wait — perhaps A, B, and F — but not collinear.

So no three labeled points are collinear.

But perhaps the problem expects A, B, and a midpoint, but not labeled.

So likely, no answer.

But maybe A, B, and C are meant to be on a line — but not in a cube.

Wait — perhaps the diagram is not a cube, but a flat figure?

But it has 3D arrows.

Alternatively, maybe A, C, and G are on a space diagonal?

But only two points on a diagonal.

So no.

So answer: There are no three collinear points among the labeled points.

But that’s not satisfactory.

Perhaps the problem has a typo.

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Question 8:

a. How many planes?
- 6 faces: bottom, top, front, back, left, right

✔ 6

b. Name the planes:
- ABCD, EFGH, ABFE, CDHG, ADHE, BCGF

c. Name six coplanar points:
- Impossible — only 4 per face.

So perhaps four.

But it says “six”.

Unless the diagram has more points.

Alternatively, perhaps the question means “name six points that are coplanar”, and we can choose from multiple faces.

But still, only 4 per face.

So likely a typo.

Perhaps “six” is “four”.

d. Name four non-coplanar points:
- A, B, C, E — A, B, C on bottom, E above A — not coplanar.

✔ Answer: A, B, C, E

e. What is the intersection of line AB and line CD?

- AB and CD are opposite edges on the bottom face.
- AB is front edge, CD is back edge.
- They are parallel and do not intersect.

So no intersection.

But in a plane, if they are parallel, they don’t intersect.

So intersection is empty.

But if they are skew? No — in the same plane (bottom), they are parallel.

So they do not intersect.

✔ Answer: No intersection (or empty set)

But if the diagram shows them extending, still parallel.

So no intersection.

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Question 9:

Assume a triangular prism with:
- Base: W, X, Y
- Top: A, B, C
- Lateral edges: WA, XB, YC

Then:

a. Name six coplanar points:
- Only four per face.

So impossible.

But if we consider all points on the same plane, but no such plane.

So likely, the question means four.

But it says “six”.

Alternatively, perhaps the diagram has more points.

Or perhaps “six” is a mistake.

b. Name four non-coplanar points:
- W, X, Y, A — W,X,Y on base, A on top — not coplanar.

✔ Answer: W, X, Y, A

c. How many planes are in the diagram?

- 2 bases: WXY, ABC
- 3 lateral faces: WABX, XBCY, YWAC

Total: 5 planes

✔ Answer: 5

d. Name three collinear points:
- On an edge: W, A, and a midpoint — but not labeled.

So no.

But if we assume WA is a line, then W and A are on it, but only two points.

So no three collinear.

But perhaps W, A, and a point on WA — not labeled.

So likely, none.

But if the diagram has a point on WA, say P, then W, P, A are collinear.

But not labeled.

So probably no answer.

e. Are planes W and ABC different planes?

- “Planes W” — probably means plane WXY (the base)
- Plane ABC is the top
- So yes, different planes.

✔ Answer: Yes

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Final Answers Summary:

#### Question 7:
a. Yes, A, C, E are coplanar.
b. AB, AD, AE (example)
c. No three labeled points are collinear.
d. No intersection (parallel lines)

#### Question 8:
a. 6 planes
b. ABCD, EFGH, ABFE, CDHG, ADHE, BCGF
c. Cannot name six coplanar points (only four per face)
d. A, B, C, E (non-coplanar)
e. No intersection

#### Question 9:
a. Cannot name six coplanar points
b. W, X, Y, A (non-coplanar)
c. 5 planes
d. No three collinear points
e. Yes, planes WXY and ABC are different

#### Question 10:
Point B lies on segment YZ — so B is between Y and Z.

#### Question 11:
Plane J contains line s means every point on line s is in plane J.

#### Question 12:
Lines r and t intersect at point Z.

#### Question 13:
Rays JK and CD intersect at a point; Y is not on either ray.

#### Question 14:
Lines M and N intersect at point J (since $\overline{JJ}$ is just point J).

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If you can provide the actual image or clarify the diagrams, I can give more accurate answers. But based on typical geometry problems, this is the best interpretation.