Free Lines Rays and Line Segments Worksheet | 10+ Pages - Free Printable

Let's analyze the given complex figure step by step and answer each question carefully.

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Given Figure Description:

We have a geometric figure with several lines, rays, line segments, and points labeled:

- Points: A, B, C, D, E, N, O
- Lines and rays intersecting at point O
- Arrows indicate rays (infinite in one direction)
- Some segments are finite (e.g., ON, DB)

Let’s go through each part.

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i) Name the two intersecting lines?

Answer:
The two lines that intersect at point O are:

- Line AB (horizontal line passing through A, O, B)
- Line CE (diagonal line passing through C, O, E)

These two lines cross at point O, so they are intersecting lines.

✔ Answer:
→ Line AB and Line CE

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ii) How many line segments in the above figure?

A line segment has two endpoints.

Let’s list all possible line segments:

1. AO (from A to O)
2. OB (from O to B)
3. OC (from O to C)
4. OE (from O to E)
5. OD (from O to D)
6. ON (from O to N)
7. DB (from D to B)
8. CD (from C to D) — Wait, is CD a segment?

Wait! Let's clarify:

- C and D are on the same horizontal line.
- But CD is part of the line that goes from left to right through C and D.
- However, C and D are both on the same line, but CD is not directly connected unless it's drawn.

Looking closely:
- There is a horizontal line with arrows at both ends → this is a line, not a segment.
- But D and B are connected by a vertical segment.
- C and D lie on a horizontal line, but no direct segment between them is drawn; instead, the line passes through both.

But we see:
- DB is a vertical line segment from D to B.
- ON is a segment from O to N.
- AO, OB, OC, OE, OD are all segments from O to other points.

Also:
- Is CD a segment? No, because C and D are just points on a line, but there's no indication of a segment between them.
- Similarly, AB is a line with arrows, so it's infinite, but AO and OB are parts of it.

So, the actual line segments are:

1. AO
2. OB
3. OC
4. OE
5. OD
6. ON
7. DB

Is there any more?

Wait: What about CD? No — no segment drawn between C and D.

What about DE or CE? CE is a line, but OE and OC are already counted.

Now, check if OD and DB form a path? But they're separate.

But note: D is connected to B via DB, and D is also on the horizontal line.

But DB is clearly a segment.

Also, is BD same as DB? Yes.

Now, is CO same as OC? Yes.

So total line segments:

- AO
- OB
- OC
- OE
- OD
- ON
- DB

That’s 7 segments.

Wait — is AB a segment? No, because it's a line with arrows on both sides.

Similarly, CE is a line with arrows.

But AO and OB are parts of AB — but since they are finite, they are segments.

So only finite portions between two points are segments.

So let’s list all distinct line segments:

1. AO
2. OB
3. OC
4. OE
5. OD
6. ON
7. DB

Is there CD? No — no direct connection.

Is CB or BE? No.

So total = 7 line segments

✔ Answer:
→ 7

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iii) Is there any parallel line, Name them

Look for lines that never meet and are equidistant.

We see:

- The horizontal line through A, O, B (let's call it line AB)
- The horizontal line through C, D — but wait, does it pass through D?

Yes — there is a horizontal line going through C and D, and it has arrows on both ends → so it's a line.

And another horizontal line going through A, O, B — also with arrows.

So these two horizontal lines are parallel.

They are both horizontal and don't intersect.

So:

- Line AB (through A, O, B)
- Line CD (through C, D)

Are they parallel? Yes.

✔ Answer:
→ Yes, line AB and line CD are parallel

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iv) Shortest line segment

Look at the segments:

- AO – appears long
- OB – similar
- OC – medium
- OE – longer
- OD – medium
- ON – very short
- DB – vertical, medium

Among all, ON is the shortest segment — it's a small segment from O to N.

✔ Answer:
→ ON

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v) ON is perpendicular to

Check angle between ON and other lines.

ON is a downward-sloping segment from O to N.

Now, look at DB: it’s a vertical segment from D to B.

But ON is not vertical.

Wait — look at DB: it's vertical.

Now, ON is not perpendicular to DB.

But what about AB? AB is horizontal.

ON is going down-left — not vertical.

Wait — perhaps ON is perpendicular to DB?

No — DB is vertical, ON is diagonal.

But look: is ON perpendicular to AB?

AB is horizontal.

ON is slanting downward — not vertical or horizontal.

Wait — perhaps ON is perpendicular to CD?

CD is horizontal.

Same issue.

Wait — maybe ON is perpendicular to DB?

But DB is vertical, ON is not horizontal.

But visually, ON seems to be going straight down from O to N — almost vertical?

Wait — actually, looking at the figure:

- ON is a short segment from O to N, pointing downward, and it looks like it might be perpendicular to AB?

But AB is horizontal, so if ON were vertical, it would be perpendicular.

But ON is not vertical — it's slightly angled.

Wait — but DB is vertical, and ON is not vertical.

But ON is shorter and pointing down — but not aligned.

Wait — perhaps ON is perpendicular to CD? CD is horizontal → if ON were vertical, yes.

But it's not.

Wait — look again: DB is vertical, and ON is not.

But ON is not aligned with anything.

Wait — perhaps ON is perpendicular to AB?

But AB is horizontal → so only vertical lines are perpendicular to it.

But ON is not vertical.

Wait — maybe I'm missing something.

Wait — look at DB: it's a vertical segment from D to B.

But ON is not vertical.

But is ON perpendicular to AB?

No — unless it's vertical.

But it's not.

Wait — perhaps ON is perpendicular to CE?

CE is diagonal.

But no.

Wait — perhaps ON is not perpendicular to any?

But the question says "ON is perpendicular to" — implying it is.

Wait — maybe ON is perpendicular to DB?

But DB is vertical, ON is not.

Wait — unless ON is vertical.

Looking at the diagram: ON is a short line going down from O to N — and it's drawn vertically downward.

Yes — in the figure, ON is vertically downward.

And DB is vertical too.

But then ON and DB are both vertical → they are parallel, not perpendicular.

Wait — but AB is horizontal.

If ON is vertical, then it is perpendicular to AB.

Yes!

Because:

- AB is horizontal
- ON is vertical
- So they are perpendicular

Even though they don’t intersect at O? Wait — ON starts at O, which is on AB.

So ON starts at O (on AB) and goes vertically down.

So ON is perpendicular to AB.

✔ Answer:
→ AB

(Or more precisely, ON is perpendicular to line AB)

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vi) How many rays are there in the above figure?

A ray has one endpoint and extends infinitely in one direction.

Look for arrows — they indicate rays.

Count the rays:

1. From A to the left → ray starting at A, going left (arrow)
2. From B to the right → ray starting at B, going right (arrow)
3. From C to the left → ray starting at C, going left (arrow)
4. From D to the right → ray starting at D, going right (arrow)
5. From E to the right → ray starting at E, going right (arrow)
6. From C to the top-left → ray from C going up-left (arrow)
7. From D to the top-right → ray from D going up-right (arrow)
8. From E to the bottom-right → ray from E going down-right (arrow)

Wait — let’s list all endpoints with arrows.

From the figure:

- At A: arrow to the left → ray ←A
- At B: arrow to the right → ray B→
- At C: arrow to the left → ray ←C
- At D: arrow to the right → ray D→
- At E: arrow to the right → ray E→
- Also, at C: arrow upward-left → ray from C going up-left
- At D: arrow upward-right → ray from D going up-right
- At E: arrow downward-right → ray from E going down-right

But are these all distinct rays?

Let’s identify each ray:

1. Ray starting at A, going left → ray AX (say)
2. Ray starting at B, going right → ray BY
3. Ray starting at C, going left → ray CZ
4. Ray starting at D, going right → ray DW
5. Ray starting at E, going right → ray EX
6. Ray starting at C, going up-left → ray CU
7. Ray starting at D, going up-right → ray DV
8. Ray starting at E, going down-right → ray ER

But wait — are CZ and CU both from C?

Yes — two rays from C: one left, one up-left.

Similarly, D has two rays: right and up-right.

E has two rays: right and down-right.

But A has one ray: left.

B has one ray: right.

So total:

- A: 1 ray
- B: 1 ray
- C: 2 rays
- D: 2 rays
- E: 2 rays

Total = 1 + 1 + 2 + 2 + 2 = 9 rays

But wait — are the lines themselves considered rays?

For example, the horizontal line through A and B has arrows on both ends — but that means it's a line, not a ray.

But rays are parts of lines with one endpoint.

So only the parts with arrows starting from a point count.

So yes — each arrow indicates a ray.

So count:

1. Left from A → ray
2. Right from B → ray
3. Left from C → ray
4. Right from D → ray
5. Right from E → ray
6. Up-left from C → ray
7. Up-right from D → ray
8. Down-right from E → ray

Wait — that’s 8 rays.

But earlier I said 9.

Wait — A has one ray (left), B has one (right), C has two (left and up-left), D has two (right and up-right), E has two (right and down-right).

So:

- A: 1
- B: 1
- C: 2
- D: 2
- E: 2

Total = 1+1+2+2+2 = 8 rays

But wait — C has two arrows: one to the left, one to the top-left.

Yes.

Similarly, D: one to the right, one to the top-right.

E: one to the right, one to the bottom-right.

So yes — 8 rays.

But is there a ray from O? No — no arrow from O.

Only from A, B, C, D, E.

So total 8 rays.

✔ Answer:
→ 8

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✔ Final Answers:

i) Name the two intersecting lines?
→ Line AB and Line CE

ii) How many line segments in the above figure?
→ 7

iii) Is there any parallel line, Name them
→ Yes, line AB and line CD are parallel

iv) Shortest line segment
→ ON

v) ON is perpendicular to
→ AB

vi) How many rays are there in the above figure?
→ 8

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Let me know if you'd like a visual explanation or labeling!