Parallel And Perpendicular Lines Worksheet Fresh Math Ms Csipak S ... - Free Printable

Let's solve each problem on the worksheet step by step, based on the definitions provided:

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Definitions Recap:

- Parallel lines: Lines that never cross, even if extended. They are always the same distance apart.
- Intersecting lines: Lines that cross at a point.
- Perpendicular lines: A special type of intersecting lines that form right angles (90°) where they meet.

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Part 1: Write "parallel" or "not parallel" for each.

#### 1. Lines TS and UV
- These two lines are slanted in the same direction and appear to be equidistant.
- They do not cross and will not cross if extended.
✔ Answer: parallel

#### 2. Lines WX and YZ
- Both lines are vertical (up-down).
- They are straight up and down and seem to be the same distance apart.
- Since they are both vertical and parallel, they will never meet.
✔ Answer: parallel

#### 3. Lines KJ and LM
- Line KJ goes upward to the right.
- Line LM goes downward to the right.
- They are going in different directions and will eventually meet if extended.
✘ Answer: not parallel

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Part 2: Write "parallel", "intersecting", or "perpendicular" for each.

#### 4. Lines PQ and NO
- Line PQ is horizontal.
- Line NO is diagonal (going down to the right).
- They cross at one point.
- No right angle is shown.
✔ Answer: intersecting

#### 5. Lines FG and HI
- Both lines are slanted in the same direction.
- They appear to be equidistant and will never meet.
✔ Answer: parallel

#### 6. Lines BD and FC
- Both lines are nearly vertical but slightly curved.
- However, looking closely, they appear to converge toward a point.
- They are not perfectly parallel; they seem to meet if extended.
- But no right angle is shown.
✔ Answer: intersecting
*(Note: Though they look almost parallel, slight deviation suggests they'll intersect unless explicitly parallel — here, they’re not perfectly aligned, so we assume they intersect.)*

#### 7. Lines ST and VU
- The lines cross, and there is a square box (right angle symbol) at the intersection.
- This indicates they form a 90° angle.
✔ Answer: perpendicular

#### 8. Lines AB and CD
- Both lines start from a common point (B and C), but go in different directions.
- They diverge and don’t cross again.
- They are not parallel (different slopes), and they only meet at one point — but that’s just a vertex.
- Wait: these are rays starting from B and C, but not overlapping.
- Actually, they don't cross except possibly at their endpoints?
- Looking closely: AB starts at A and goes through B; CD starts at D and goes through C.
- They do not intersect unless extended — but as drawn, they don't meet.
- But they are not parallel either — different directions.
- So, they are not intersecting, and not parallel → but the question asks to choose among parallel, intersecting, or perpendicular.
- Since they do not intersect and are not parallel, the correct classification is:
⚠️ But wait — in geometry, if two lines (or rays) don’t intersect and aren't parallel, they are neither — but this worksheet seems to expect one of the three.

But let's recheck: Are they intersecting? Only if they cross. As drawn, they don’t cross. Are they parallel? No. So neither?

But since the options are only these three, and they are not parallel and don’t intersect, perhaps the answer is not applicable — but likely the intention is to say not parallel, but the instruction says to pick from parallel, intersecting, or perpendicular.

Wait — actually, AB and CD are two separate rays that do not cross, and are not parallel, so they are not intersecting, not parallel, and not perpendicular.

But since the worksheet forces a choice, and they don't cross, they are not intersecting.

But the answer must be one of the three.

Actually, they are not intersecting, and not parallel — so none apply.

But perhaps the diagram shows them as diverging rays, which are not intersecting.

So if they don’t intersect, then they can't be intersecting or perpendicular.

But only parallel lines never intersect — others may or may not.

But if they don’t intersect, they could still be parallel or non-parallel non-intersecting (but in plane geometry, two lines either intersect or are parallel).

Ah! Key point: In Euclidean geometry, two lines in a plane either intersect or are parallel.

So if two lines do not intersect, they must be parallel.

But in this case, AB and CD are not parallel — they have different slopes.

So how can they not intersect and not be parallel?

Because they are rays, not full lines.

So rays can be non-parallel and not intersecting if they don’t extend to meet.

So in this case, AB and CD are not parallel, don’t intersect, so neither.

But the worksheet expects one of the three.

Looking at the image: Rays AB and CD start from points A and D, go through B and C, respectively. They are diverging — so they will never meet.

But they are not parallel.

So the correct answer is not parallel, but since the option isn't available, and the instruction says to write parallel, intersecting, or perpendicular, we must conclude they are not any of those — but that's not allowed.

Wait — perhaps I misread.

Look again: Ray AB goes from A to B, continuing beyond B.

Ray CD goes from C to D, continuing beyond D.

They are not extending toward each other — they are moving away.

So they never intersect, and are not parallel.

But in plane geometry, if two lines (infinite) are not parallel, they must intersect.

But these are rays, not lines.

So rays can be non-parallel and non-intersecting.

So the correct classification is neither, but the worksheet doesn't allow that.

But perhaps the intended answer is not parallel, but the instruction says to pick from parallel, intersecting, or perpendicular.

So maybe the teacher expects not parallel, but that’s not an option.

Wait — perhaps I made a mistake.

Let me re-express:

- If two lines are not parallel, they intersect.
- But rays can be non-parallel and not intersecting if they don’t extend into each other’s path.

But in this case, the rays are diverging — so they won’t meet.

But the worksheet likely treats them as lines, not rays.

So if we consider line AB and line CD, then:

- They are not parallel (different slopes)
- So they must intersect somewhere — but not in the diagram.

But since they are not parallel, and not perpendicular, and intersect, then:

✔ Answer: intersecting

But do they intersect? Let's see:

- Ray AB: from A to B, going down-right
- Ray CD: from D to C, going down-left

Wait — the labels: A→B is up-right? No.

From the diagram:

- A is above B, and arrow is pointing down from A to B — so ray AB goes from A down to B and continues down.
- Similarly, D is above C, and arrow from D to C — so ray DC goes down.

But the ray is labeled CD — so from C to D? Wait, the arrow is pointing from D to C? Or C to D?

Look: The line has arrowheads at both ends? No — it’s a ray.

In #8: Ray AB has arrowhead at B (so from A to B and beyond). Ray CD has arrowhead at D (from C to D and beyond).

So:
- AB: starts at A, goes through B, continues beyond B.
- CD: starts at C, goes through D, continues beyond D.

Now, looking at direction:
- AB: going down and to the right
- CD: going down and to the left

So they are diverging — never meet.

And not parallel.

So they are not parallel, not intersecting, not perpendicular.

But the worksheet wants one of the three.

This is ambiguous.

But in most such worksheets, if two lines (rays) do not cross and are not parallel, they are considered not parallel, but the answer must be chosen from the three.

Alternatively, perhaps the rays are meant to be lines.

If we treat them as infinite lines, then:

- Line AB and line CD — if extended, would they intersect?

Yes — because they are not parallel, so in a plane, they must intersect.

So intersecting.

But in the diagram, they don’t cross — but that’s because they are rays.

But in geometry problems like this, we consider the lines they lie on.

So line AB and line CD are not parallel → they intersect somewhere.

So ✔ Answer: intersecting

Similarly, for all cases, we consider the lines.

So for #8: intersecting

#### 9. Lines JK and LM
- Line JK is horizontal.
- Line LM is vertical.
- They cross at point M.
- There is a right angle symbol at the intersection.
✔ Answer: perpendicular

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✔ Final Answers:

#### Part 1: Parallel or Not Parallel
1. parallel
2. parallel
3. not parallel

#### Part 2: Parallel, Intersecting, or Perpendicular
4. intersecting
5. parallel
6. intersecting
7. perpendicular
8. intersecting
9. perpendicular

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✔ Summary:

| Question | Answer |
|--------|----------------|
| 1 | parallel |
| 2 | parallel |
| 3 | not parallel |
| 4 | intersecting |
| 5 | parallel |
| 6 | intersecting |
| 7 | perpendicular |
| 8 | intersecting |
| 9 | perpendicular |

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📝 Explanation Recap:

- Parallel: Never cross, same direction (e.g., 1, 2, 5)
- Intersecting: Cross at one point (e.g., 4, 6, 8)
- Perpendicular: Intersect at right angles (e.g., 7, 9)
- Not parallel: When lines are not parallel (e.g., 3)

Let me know if you'd like a printable version with answers filled in!