FREE Know the Value of Points Lines and Planes Worksheet [PDFs] - Free Printable

Let's solve the geometry worksheet step by step based on the figures provided.

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Problem 1

We are given a diagram with points A, B, C, D, E, and lines intersecting at point B.

#### a) Name all the points.
The points shown in the figure are:
- A
- B
- C
- D
- E

✔ Answer: A, B, C, D, E

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#### b) Name any three rays.
A ray starts at a point and goes infinitely in one direction.

From the diagram:
- Ray BA (starts at B, goes through A)
- Ray BC (starts at B, goes through C)
- Ray BD (starts at B, goes through D)
- Ray BE (starts at B, goes through E)

Any three of these are acceptable.

✔ Answer (example): Ray BA, Ray BC, Ray BD

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#### c) Name any two line segments.
A line segment has two endpoints.

Examples:
- Segment AB
- Segment BC
- Segment BD
- Segment BE
- Segment DE

Choose any two.

✔ Answer (example): Segment AB, Segment BC

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#### d) Name the line in two ways.
There is a straight line passing through points A, B, and C. So this is line AC (or line CA).

Also, since it passes through B, we can name it using any two points on it.

So, two names for the same line:
- Line AC
- Line BC
- Line AB

But to write it in two ways:
✔ Answer: Line AC and Line BC

> Note: We use two capital letters, and the order doesn't matter for naming a line.

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Problem 2

Now look at the second diagram with points L, O, T, M, and N, and lines intersecting at point O.

#### a) Name the line that contains the point O.
We see that point O lies on multiple lines:
- One line goes from L to T (passes through O)
- Another line goes from M to N (passes through O)

So the lines containing O are:
- Line LT
- Line MN

Since the question asks for "the line", but there are two, we assume it wants one such line.

✔ Answer: Line LT (or Line MN)

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#### b) Name the two opposite rays.
Opposite rays start at the same point and go in opposite directions along the same line.

Looking at point O:
- Ray OL and Ray OT are opposite rays because they lie on the same line (LT), starting at O and going in opposite directions.
- Similarly, Ray OM and Ray ON are opposite rays.

So two pairs:
- Ray OL and Ray OT
- Ray OM and Ray ON

✔ Answer: Ray OL and Ray OT (or Ray OM and Ray ON)

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#### c) Name the endpoint of $\overrightarrow{OE}$
Wait — there is no point E in Figure 2. But looking back, maybe it's a typo or mislabeling.

In Figure 2, the points are: L, O, T, M, N.

But the vector mentioned is $\overrightarrow{OE}$. There is no point E here.

Wait — perhaps this is a mistake in your image? Or maybe it's meant to be $\overrightarrow{OT}$ or $\overrightarrow{OM}$?

Alternatively, if the ray is $\overrightarrow{OT}$, then the endpoint is O.

But the notation $\overrightarrow{OE}$ implies a ray starting at O and going toward E — but E isn't in the diagram.

Possibility: Maybe it’s supposed to be $\overrightarrow{OT}$ or $\overrightarrow{ON}$?

Wait — let's check again. The original problem says:

> c) Name the endpoint of $\overrightarrow{OE}$

But E is not in Figure 2. That must be an error.

But wait — in Figure 1, there was point E, but in Figure 2, only L, O, T, M, N.

So unless there's a typo, this might be incorrect.

Alternatively, perhaps it's meant to be $\overrightarrow{OT}$ or $\overrightarrow{OM}$?

But since the text says $\overrightarrow{OE}$, and E is not present, we should assume it's a typo.

But let's suppose it's $\overrightarrow{OT}$ instead — then the endpoint is O.

Because in ray notation $\overrightarrow{OT}$, the endpoint is O, and it goes through T.

✔ So, the endpoint of $\overrightarrow{OT}$ is O.

But the problem says $\overrightarrow{OE}$ — so unless E is labeled somewhere else, this is likely a typo.

Alternatively, maybe in some versions, point E is labeled as T or something.

But based on the diagram, there is no point E.

Therefore, assuming a typo and it should be $\overrightarrow{OT}$, then:

✔ Answer: O

If it really is $\overrightarrow{OE}$, and E is not in the diagram, then the question cannot be answered — but that seems unlikely.

Wait — let me recheck: In Figure 2, we have points: L, O, T, M, N.

No E.

So probably, it's a typo and should be $\overrightarrow{OT}$ or $\overrightarrow{OM}$.

Let’s assume it’s $\overrightarrow{OT}$.

Then the endpoint is O.

✔ Answer: O

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#### d) Name all the points that lie on the line $\overline{ST}$
Again, there is no point S or T in the way this is drawn.

Wait — in Figure 2, we have points L, O, T, M, N.

Is “S” a typo? Is it meant to be L or M?

Wait — the line segment is written as $\overline{ST}$ — but S is not labeled.

This suggests another possible typo.

But in Figure 2, we have:
- Line LT: points L, O, T
- Line MN: points M, O, N

So if $\overline{ST}$ is meant to be $\overline{LT}$, then the points on line LT are:
- L, O, T

Similarly, if it's $\overline{MN}$, then M, O, N.

But since it says $\overline{ST}$, and S is not labeled, it's likely a typo.

Most plausible: It should be $\overline{LT}$ or $\overline{MN}$.

Assuming it's $\overline{LT}$, then the points on that line are:
- L, O, T

✔ Answer: L, O, T

Or if it's $\overline{MN}$: M, O, N

But without clarification, best guess is $\overline{LT}$.

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✔ Final Answers:

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Problem 1:

a) A, B, C, D, E
b) Ray BA, Ray BC, Ray BD (any three)
c) Segment AB, Segment BC (any two)
d) Line AC and Line BC

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Problem 2:

a) Line LT (or Line MN)
b) Ray OL and Ray OT (or Ray OM and Ray ON)
c) O (assuming $\overrightarrow{OE}$ is a typo for $\overrightarrow{OT}$ or similar)
d) L, O, T (assuming $\overline{ST}$ is a typo for $\overline{LT}$)

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⚠️ Note: There appear to be typos in the worksheet:
- Point E is not in Figure 2 → $\overrightarrow{OE}$ is invalid
- Point S is not in Figure 2 → $\overline{ST}$ is invalid

These should be corrected to match the diagram.

If you can confirm the labels, I can adjust accordingly.

Otherwise, the answers above are based on logical inference and common geometric conventions.