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. Since I can't view images directly, I'll help you solve each problem based on the text you've provided. However, for accuracy, especially with diagrams (like 3D shapes or labeled figures), it's important that the descriptions of the figures are accurate.

Let’s go through each question step by step, assuming typical geometric configurations based on common textbook diagrams (e.g., cube, pyramid, etc.).

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Question 7:

*(Assuming a diagram with points A, B, C, D, E, F, G, H — likely a cube or rectangular prism)*

a. Are points A, C, and E coplanar?
→ Answer: Yes, if they lie on the same plane. In a cube, if A, C, and E are vertices such that they lie on a face or diagonal plane, they may be coplanar. For example, if A, C, and E are three corners of a face or a diagonal plane, then yes. But without seeing the figure, we assume standard labeling:
- Let’s suppose A, C, and E are not all on the same face. If A and C are on one face, and E is opposite, they might not be coplanar.
But commonly in such problems, A, C, and E are not coplanar if they form a skew configuration.

Wait — let’s reconsider: In a cube, any three points are coplanar, unless they are not on a flat surface. But three points are always coplanar (since three non-collinear points define a plane). So:

✔ Answer: Yes, any three points are coplanar (unless specified otherwise).

> ✔ Answer: Yes

b. Name the three lines:
→ Likely referring to visible lines in the diagram. Common lines might be:
- Line AB
- Line AC
- Line AE

But since no labels are given, assume standard notation.
✔ Example answer: AB, AC, AD (or any three distinct lines)

> ✔ Answer: AB, AC, AD (example; depends on diagram)

c. Name three collinear points:
→ Collinear = lying on the same straight line.
In a cube, e.g., A, B, C may not be collinear. But if there's a line segment like A–B–C, then A, B, C are collinear.
But typically, only two points define a line. So look for a straight edge.

✔ Example: A, B, C — only if they are on a straight line (unlikely). More likely: A, B, and midpoint — but usually, no three vertices of a cube are collinear.

So maybe: No three vertices are collinear — so this might refer to points along an edge.

Suppose A and B are endpoints of an edge, and M is midpoint → A, M, B are collinear.

But since only letters are given, perhaps the diagram includes labeled points.

✔ Answer: A, B, C — only if they are on a straight line. Otherwise, A, B, and a point on AB.

But since the problem says "name three collinear points", and only vertices are labeled, likely no three are collinear.

Wait — in a cube, no three vertices are collinear.

So perhaps the diagram shows something else — like a pyramid or a different shape?

Alternatively, maybe A, B, C are on a diagonal?

No — in a cube, diagonals connect opposite corners, but three vertices aren’t collinear.

✔ Conclusion: There are no three collinear vertices in a cube.

So possibly, the diagram has additional points (like midpoints).

But since it's not specified, assume:
✔ Answer: A, B, and M (if M is midpoint) — but not labeled.

So perhaps the diagram includes points like A, B, C on a line.

Wait — maybe it's a 2D drawing?

Given ambiguity, assume:
✔ Answer: A, B, and C — if they lie on a straight line in the diagram.

But again, without image, we must assume.

Perhaps in Question 7, it's a triangle or coordinate plane?

Wait — there's an arrow pointing up from a point — maybe a 3D coordinate system?

Let’s move to Question 8 — which seems clearer.

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Question 8:

*(Likely a cube or rectangular prism 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 may be diagonal planes (like internal ones), but usually, only faces are counted.

✔ Answer: 6 planes (the six faces)

b. Name the planes:
→ Typically:
- Plane ABCD (bottom face)
- Plane EFGH (top face)
- Plane ABFE (front)
- Plane BCGF (right)
- Plane CDHG (back)
- Plane DAEH (left)

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

c. Name six coplanar points:
→ Any six points on one face are coplanar.

For example: A, B, C, D, E, F — but E and F are on top, so not on bottom.

Better: Points on one face: A, B, C, D, E, F — no, E and F are above.

Actually, each face has 4 points.

So maximum 4 coplanar points per face.

So “six coplanar points” is impossible unless more than 4 are on a single plane.

But in a cube, only 4 vertices per face.

So unless the diagram includes midpoints, you cannot have six coplanar points.

Wait — maybe the diagram shows a plane cutting through multiple points?

Alternatively, perhaps A, B, C, D, E, F are not all on one face.

So likely, the question means any six points that lie on a single plane — but in a cube, no plane contains six vertices.

So perhaps the diagram is not a cube, or includes more points.

Alternatively, maybe it’s asking for six points that are coplanar, even if not all on a face.

But still, in a cube, maximum four vertices per plane.

So perhaps the diagram includes midpoints.

But since not specified, maybe the answer is:

✔ Answer: A, B, C, D, E, F — if they lie on a single plane (but they don’t).

So perhaps the intended answer is:

✔ Answer: A, B, C, D, E, F — but only if they are on a single plane.

Alternatively, maybe A, B, C, D, G, H — no.

Wait — maybe A, B, C, D, E, F are not all on one plane.

So perhaps the question allows any six points that are coplanar — but in a cube, only four vertices per face.

So likely, the answer is:

✔ Answer: A, B, C, D — only four.

But the question asks for six.

So maybe the diagram includes intersections or additional points.

Alternatively, maybe it’s a different figure — like a pyramid?

Wait — Question 9 has a pyramid.

Let’s skip ahead.

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Question 9:

*(Diagram shows a pyramid with base ABCD and apex V, and points W, X, Y, Z)*

From the description:
- Base: quadrilateral ABCD
- Apex: V
- Points: W, X, Y, Z — likely midpoints or intersections

a. Name four non-coplanar points:
→ Non-coplanar = not lying on the same plane.

Any four points where one is off the base.

For example: A, B, C, V — A, B, C are on base, V is above → not coplanar with A,B,C unless V is on base.

So: A, B, C, V are non-coplanar (V is not on base plane).

✔ Answer: A, B, C, V

b. How many planes are in the diagram?
→ Each face is a plane:
- Base: ABCD (1 plane)
- Faces: VAB, VBC, VCD, VDA (4 triangular faces)
- Possibly internal planes, but usually only faces count.

So total: 5 planes

✔ Answer: 5 planes

c. Name three collinear points:
→ Look for points on a straight line.

Possibly: A, W, B — if W is midpoint of AB → then A, W, B are collinear.

Or: V, W, X — if W and X are on edges from V.

But if W is on AB, X on BC, then V, W, X may not be collinear.

But if W is intersection of diagonals, or something.

But likely: A, W, B — if W is midpoint of AB.

✔ Answer: A, W, B

d. Are planes W and ABC different planes?
→ Wait: "Planes W" — probably typo. Should be plane W? Or plane VWX?

Likely: Plane W is not a valid name. Probably meant plane VAB or plane WXY.

But it says: “Are planes W and ABC different planes?”

This suggests W is a plane.

But W is a point.

So likely a typo: should be plane VAB or plane VAC?

Alternatively, maybe W is a plane label — but unusual.

Possibly: plane W refers to a plane containing point W.

But ambiguous.

Wait — in some texts, points are used to label planes.

But more likely: plane VAB vs plane ABC

Then: Yes, they are different planes.

✔ Answer: Yes, plane VAB and plane ABC are different.

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Question 10:

“Now it's your turn to draw…”
“Point B on $\overline{PQ}$”

→ Draw point B somewhere on the line segment PQ.

✔ Instructions: Draw a line segment PQ, and place point B anywhere between P and Q.

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Question 11:

“Plane J containing line s.”

→ Draw a plane (a flat surface), and draw line s lying entirely within it.

✔ Instructions: Draw a rectangle (representing plane J), and draw a line s inside it.

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Question 12:

“Lines r and t intersect at pt Z.”

→ Draw two lines crossing at point Z.

✔ Instructions: Draw two lines crossing at a point labeled Z.

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Question 13:

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

→ Draw ray JK (starting at J, going through K), line segment CD, and they intersect at some point.

Also, point Y is not on either line.

✔ Instructions: Draw ray JK and segment CD so they cross. Then draw point Y somewhere away from both.

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Question 14:

“Lines m and n intersect at $\overline{TT}$”

→ This is incorrect notation. $\overline{TT}$ is a line segment from T to T — which is just a point.

So likely, it should be: intersect at point T

✔ Answer: Lines m and n intersect at point T.

So the notation $\overline{TT}$ is invalid — it's degenerate.

So correct version: Lines m and n intersect at point T

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## ✔ Summary of Answers:

7.

a. Yes — any three points are coplanar.
b. AB, AC, AD (example)
c. A, B, C — only if collinear (but in cube, not likely); otherwise, no three vertices are collinear → so maybe A, B, and midpoint — but not labeled.
d. Intersection of AB and CD: Only if they intersect — in a cube, AB and CD are opposite edges — may be skew or parallel.
If AB and CD are opposite edges, they do not intersect.
So answer: No intersection (they are skew or parallel)

✔ Answer: No intersection (if AB and CD are skew or parallel)

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8.

a. 6 planes (faces of cube)
b. ABCD, EFGH, ABFE, BCGF, CDHG, DAEH
c. A, B, C, D, E, F — but only 4 per face → impossible unless extra points.
Maybe: A, B, C, D, M, N — but not labeled.
So likely: A, B, C, D — but question asks for six → error?
Alternative: Maybe the diagram has 6 points on a plane — but unlikely.

Wait — perhaps the question is asking for six points that are coplanar, meaning any six that lie on a single plane — but in cube, max 4.

So perhaps the diagram is not a cube — maybe a flat net or 2D figure?

Alternatively, maybe A, B, C, D, E, F are on a single plane — but in a cube, they’re not.

So likely: No six points are coplanar — but that contradicts the question.

So perhaps the diagram includes midpoints.

Let’s assume: A, B, C, D, M, N — but not labeled.

So best guess: A, B, C, D, E, F — but they are not coplanar.

So perhaps the answer is: A, B, C, D, E, F — with explanation that they are not all coplanar — but that’s wrong.

Alternatively, maybe the diagram is a triangular prism or other.

Given ambiguity, perhaps the intended answer is:

✔ Answer: A, B, C, D, E, F — if they are on a single plane.

But better: A, B, C, D — only four.

So likely, the question means: Name six points that are coplanar — and the diagram has a plane with six points (e.g., including midpoints).

But since not specified, we’ll skip.

d. Name four non-coplanar points:
→ A, B, C, V (if V is apex)

✔ Answer: A, B, C, V

e. How many planes?
→ 5 (base + 4 lateral faces)

✔ Answer: 5

f. Name three collinear points:
→ A, W, B — if W is midpoint of AB

✔ Answer: A, W, B

g. Are planes W and ABC different planes?
→ Likely typo: should be plane VAB vs plane ABC

✔ Answer: Yes

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## Final Answers (Best Guess Based on Standard Diagrams):

7.

a. Yes
b. AB, AC, AD
c. A, B, C (if collinear) — but in cube, none are — so perhaps no such points
d. No intersection (AB and CD are skew or parallel)

8.

a. 6
b. ABCD, EFGH, ABFE, BCGF, CDHG, DAEH
c. A, B, C, D, E, F — but not coplanar — so maybe A, B, C, D, M, N — not labeled — so cannot determine
d. A, B, C, V
e. 5
f. A, W, B
g. Yes

9.

a. A, B, C, V
b. 5
c. A, W, B
d. Yes

10. Draw point B on segment PQ

11. Draw plane J with line s inside it

12. Draw lines r and t crossing at Z

13. Draw ray JK and segment CD intersecting, with Y off both

14. Lines m and n intersect at point T (not $\overline{TT}$ — typo)

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Please confirm the diagrams or provide more details (like labels or descriptions) for more accurate answers!