Geometry Figures -1 worksheet - Free Printable

Let's solve each question step by step using the geometric figure and symbolic notations.

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Understanding the Symbols:

In geometry, different symbols represent different types of figures:

- Ray: A ray starts at a point and extends infinitely in one direction.
Symbol: `→` above the segment (e.g., $\overrightarrow{AB}$)

- Line Segment: A finite line between two points.
Symbol: A bar with dots on both ends (e.g., $\overline{AB}$)

- Line: A straight path that extends infinitely in both directions.
Symbol: Double-headed arrow (e.g., $\overleftrightarrow{AB}$)

- Angle: Represented by the angle symbol `<` (e.g., $<ABC$)

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Now let’s analyze each question based on the diagram.

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1. Identify the correct symbolic notation for SE.

Look at the figure:
- Point S is the origin.
- E is a point extending from S with an arrow pointing toward E → this indicates a ray starting at S and going through E.

So, SE is a ray starting at S and going through E.

✔ Correct notation: $\overrightarrow{SE}$

Answer: a. $\overrightarrow{SE}$

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2. Identify the correct symbolic notation for XR.

- X and R are points on a horizontal line.
- There are arrows on both ends, meaning it extends infinitely in both directions → this is a line.

So, XR represents a line passing through X and R.

✔ Correct notation: $\overleftrightarrow{XR}$

Answer: c. $\overleftrightarrow{XR}$

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3. Identify the correct symbolic notation for PM.

- P and M are points.
- There is an arrow only at the M end, but no arrow at P → wait, actually, looking closely:
- The figure shows a line from M to P, with an arrow at M (pointing left), and P is a point on a horizontal line.
- But the segment PM is shown as a line segment from P to M, with no arrows — it’s just a line connecting them.

Wait — let's recheck:
Looking at the diagram:
- M is connected to P by a horizontal line.
- At M, there is an arrow pointing left (←), which means the ray starts at P and goes through M? No — actually, the arrow is at M, so if it's pointing away from P, then it's a ray starting at P and going through M, but the arrow is at M.

But here's the key: The arrow is at M, and it's pointing left, toward M. That suggests the ray starts at P and goes through M, with the arrow indicating direction.

Wait — actually, the arrow is at M, and it's pointing left, so the ray starts at M and goes toward P? No — the arrow is at the end, so if the arrow is at M, then the ray ends at M?

Wait — standard convention: The arrow is at the end of the ray, showing direction.

But in this case, the arrow is at M, and it's pointing left, which is toward P. So the ray starts at M and goes toward P?

But that doesn’t make sense because P is between M and S, and the arrow is pointing from M to P.

Actually, the arrow is at M, and it's pointing left, so the ray is starting at M and going toward P and beyond? But the segment is drawn from M to P, and the arrow is at M, so it's likely a ray starting at M and going through P?

No — the arrow is at M, pointing toward the left, so it's from M to P.

But the ray should be named with the endpoint first.

So if the ray starts at M and goes through P, it would be $\overrightarrow{MP}$

But the question asks for PM, which would mean starting at P and going through M.

But the arrow is at M, not at P.

Wait — look again: The figure shows a line from M to P, with an arrow at M, pointing left. So the ray starts at M and goes through P? No — if the arrow is at M, and it's pointing left, then it's going away from P, but M is on the left, P is on the right.

Wait — coordinates: M is to the left of P. Arrow at M is pointing left, so the ray is starting at M and going left — but that would be opposite to P.

So the ray is not going toward P.

Wait — maybe I'm misinterpreting.

Actually, the segment from M to P has a dot at M and a dot at P, and an arrow at M pointing left — so the ray starts at M and goes to the left, not toward P.

But that contradicts the label "PM".

Wait — perhaps the segment PM refers to the line from P to M.

But the arrow is at M, pointing left, so it's a ray starting at M, going left.

But the label is PM, which implies from P to M.

This is confusing.

Wait — let’s look carefully:

- M is on the far left.
- P is to the right of M.
- There is a horizontal line from M to P.
- At M, there is an arrow pointing left.
- At P, there is no arrow.

So the ray starts at M, goes through P, and continues beyond? But the arrow is at M, pointing left — that would mean it's going away from P, not toward P.

Wait — that can't be.

Actually, the arrow is at M, and it's pointing left, so the ray starts at M and goes to the left, not toward P.

But then why is it labeled PM?

Wait — maybe the label PM refers to the segment from P to M.

But the arrow is at M, pointing left — so the ray is starting at M and going left.

But PM would be from P to M.

This is inconsistent.

Wait — perhaps the arrow at M is part of the ray MP, but the question is asking for PM.

Let me re-express:

- The figure shows a horizontal line from M to P.
- There is an arrow at M, pointing left — so the ray starts at M and goes leftward — but that would be away from P.

That makes no sense.

Wait — unless the arrow is meant to be at the end of the ray, so if the ray is from P to M, then the arrow would be at M.

Yes! That makes sense.

So: Ray PM starts at P, goes through M, and the arrow is at M, indicating direction.

So even though M is to the left of P, the ray starts at P, goes through M, and continues beyond M.

So the notation for a ray from P to M is $\overrightarrow{PM}$

✔ So the correct symbolic notation is: $\overrightarrow{PM}$

Answer: a. $\overrightarrow{PM}$

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4. Identify the correct symbolic notation for PH.

- P and H are points.
- H is directly below P.
- There is a vertical line from P to H.
- At H, there is no arrow, but at P, there is no arrow either.
- But wait — the segment from P to H: is it a ray or a segment?

Looking at the figure:
- P is above H.
- The line goes from P down to H.
- At H, there is no arrow, but at P, there is no arrow either.

Wait — but earlier, for PM, we saw an arrow at M, which was the endpoint.

Here, at H, there is no arrow, and at P, there is no arrow.

But wait — in the diagram, H is at the bottom, and there is no arrow at H, but P is above, and there is no arrow at P.

But the segment from P to H is vertical, and there is no arrow at either end.

So it's just a line segment.

Therefore, PH is a segment.

So correct notation: $\overline{PH}$

✔ Answer: b. $\overline{PH}$

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✔ Final Answers:

1. a. $\overrightarrow{SE}$
2. c. $\overleftrightarrow{XR}$
3. a. $\overrightarrow{PM}$
4. b. $\overline{PH}$

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🔍 Summary of Reasoning:

| Question | Figure | Type | Notation |
|--------|--------|------|---------|
| 1. SE | Ray from S to E (arrow at E) | Ray | $\overrightarrow{SE}$ |
| 2. XR | Line through X and R (arrows at both ends) | Line | $\overleftrightarrow{XR}$ |
| 3. PM | Ray from P to M (arrow at M) | Ray | $\overrightarrow{PM}$ |
| 4. PH | Segment from P to H (no arrows) | Segment | $\overline{PH}$ |

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✔ Final Answers:
1. a
2. c
3. a
4. b