Parallel Lines & Angles worksheet - Free Printable

Let's go through each diagram one by one and identify the type of angles (corresponding, alternating, or co-interior) based on their positions relative to the parallel lines and the transversal.

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Key Definitions:

- Corresponding angles: Angles that are in the same relative position at each intersection where a straight line crosses two others. They form an "F" shape.
- Alternating angles (Alternate interior/exterior): Angles that are on opposite sides of the transversal and between (interior) or outside (exterior) the parallel lines. They form a "Z" or "N" shape.
- Co-interior angles (Consecutive interior angles): Angles that are on the same side of the transversal and inside the parallel lines. They form a "C" or "U" shape and add up to 180° if the lines are parallel.

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Now, let’s analyze each diagram:

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1.

```
/\
/__\
/____\
```
Two parallel lines cut by a transversal. The blue angles are both on the same side of the transversal and between the parallel lines.

- These are co-interior angles (also called consecutive interior angles).

✔ Type of angles: Co-interior

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2.

```
/
/
/__ __/
/_____/_____
```
Two parallel lines with a transversal. The blue angles are on opposite sides of the transversal and outside the parallel lines.

- This forms a "Z" shape — these are alternate exterior angles.

✔ Type of angles: Alternating (alternate exterior)

> Note: "Alternating" is often used as shorthand for "alternate".

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3.

This diagram has two pairs of angles:
- Blue angles: On opposite sides of the transversal and between the parallel lines → "Z" shape → Alternate interior angles
- Green angles: On same side of the transversal and inside the lines → "C" shape → Co-interior angles

✔ Type of angles (blue): Alternating (alternate interior)
✔ Type of angles (green): Co-interior

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4.

- Blue angles: On opposite sides of the transversal, between the lines → "Z" shape → Alternate interior angles
- Green angles: On same side, outside the lines → "C" shape but on the outside → Co-exterior angles, but usually we refer to them as co-interior only when inside.

Wait — actually, green angles are on the same side of the transversal and outside the parallel lines. So they are co-exterior angles (not standard terminology), but more accurately, they are same-side exterior angles.

But since the question asks for corresponding, alternating, or co-interior, and co-interior refers specifically to interior angles on the same side, we should classify:

- Blue angles: Alternate interior → Alternating
- Green angles: Same side, outside → Not typically classified as co-interior. But since they are on the same side and outside, they are co-exterior, which isn't listed. However, if the options are limited, perhaps they are corresponding?

Wait — let's check: Are green angles corresponding?

No — they are not in the same relative position.

Actually, looking closely: the green angles are on the same side of the transversal and outside the lines → they are same-side exterior angles. But this category is not among the three given.

But wait — perhaps they are corresponding? No — they are not matching positions.

Alternatively, maybe they are alternating? No — not opposite.

So likely, the green angles are co-exterior, but since that's not an option, and the instruction says to pick from corresponding, alternating, or co-interior, then:

- Blue angles: Alternate interior → Alternating
- Green angles: They are not co-interior (they’re outside). But they might be corresponding?

Wait — no. Let’s look carefully.

Actually, upon inspection, the green angles are on the same side of the transversal and outside the lines. So they are same-side exterior angles. But this is not one of the three categories.

However, sometimes “co-interior” is used loosely, but strictly speaking, it applies only to interior angles.

So, unless there’s a mistake, perhaps the green angles are corresponding?

No — they are not in the same position.

Wait — maybe they are corresponding? Let’s see: top-left vs bottom-left? No — the transversal is slanted.

Actually, the green angles are on the same side of the transversal and on the same side of the lines — so they are same-side exterior angles, which are not named in the list.

But perhaps in this context, they are considered co-interior? No — that would be incorrect.

Alternatively, maybe the green angles are corresponding? No.

Wait — perhaps I misread.

Looking again: Diagram 4 shows:

- Two parallel lines
- A transversal cutting them
- Green angles are on the top-right and bottom-right, both on the same side of the transversal, and outside the lines.

So they are same-side exterior angles — not corresponding, not alternating, not co-interior.

But the question asks to choose from those three.

Possibility: Maybe the green angles are corresponding?

No — corresponding angles are in the same relative position.

For example, top-left and bottom-left would be corresponding.

But here, the green angles are both on the right side, but one is above, one is below, so they are not corresponding.

They are same-side exterior, which is not in the list.

But perhaps the intended answer is co-interior? No — because they are outside.

Wait — maybe the green angles are alternating? No — they are on the same side.

Hmm.

Wait — could they be corresponding? Let's think: if you trace the transversal, the green angle on the top is on the right side of the transversal, and the bottom one is also on the right side — so they are on the same side of the transversal.

But corresponding angles are on the same side of the transversal and in the same relative position with respect to the lines.

Here, both are outside, on the right, so they are corresponding?

Yes! Wait — yes!

If the transversal cuts the lines, then angles on the same side of the transversal and in the same relative position (e.g., both upper-right or both lower-right) are corresponding.

So the green angles are both on the right side of the transversal and outside the lines — so they are corresponding angles.

✔ Green angles: Corresponding

And blue angles: On opposite sides of the transversal, between the lines → Alternate interior → Alternating

So:

✔ Type of angles (blue): Alternating
✔ Type of angles (green): Corresponding

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5.

This looks like a triangle with a line drawn from the top vertex to the base.

The two blue angles are:
- One at the top-left corner
- One at the bottom-left corner

But notice: There is a horizontal line and a diagonal line forming a transversal.

Actually, this seems like a triangle with a line parallel to the base.

Wait — the figure shows:
- A large right triangle
- A horizontal line from the left side to the hypotenuse
- Two blue angles: one at the top-left corner, one at the bottom-left corner

But they are both on the same side of the transversal (the diagonal side), and between the lines?

Wait — perhaps the horizontal line is parallel to the base?

Looking at arrows: The horizontal line has an arrow pointing right, and the base also has an arrow — suggesting they are parallel.

So we have two parallel lines (the horizontal line and the base), cut by a transversal (the left side of the triangle).

Then the two blue angles are:
- One at the top (on the upper parallel line)
- One at the bottom (on the lower parallel line)
- Both are on the same side of the transversal (left side), and inside the parallel lines?

Wait — the top blue angle is at the corner of the triangle, and the bottom one is at the base.

But both are adjacent to the vertical leg.

Actually, if the horizontal line is parallel to the base, and the vertical side is the transversal, then:

- The top blue angle is between the transversal and the upper parallel line
- The bottom blue angle is between the transversal and the lower parallel line
- Both are on the same side of the transversal (say, the right side)

Wait — but they are on the same side of the transversal and between the lines → so they are co-interior angles?

But they are not on the same side of the transversal — let's clarify.

The transversal is the vertical side.

- Top blue angle: formed by the vertical side and the upper horizontal line → located on the right side of the transversal
- Bottom blue angle: formed by the vertical side and the lower horizontal line → also on the right side of the transversal

So both are on the same side of the transversal, and between the parallel lines → so they are co-interior angles.

✔ Type of angles: Co-interior

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6.

Three parallel lines, cut by a transversal.

- Blue angles: Two angles on the same side of the transversal, and between the lines → but they are on consecutive lines.

Wait — the blue angles are:
- One on the top line
- One on the middle line
- Both are on the same side of the transversal and between the lines?

Actually, looking at the diagram:

- The blue angles are on the same side of the transversal
- And they are between the lines (i.e., interior)
- But they are not on the same pair — one is on top, one on middle

But still, they are on the same side of the transversal and inside the parallel lines → so they are co-interior angles?

But co-interior is usually defined for two parallel lines.

Here, with three lines, the concept extends.

But the blue angles are not on the same pair — but they are on the same side of the transversal and between the lines.

Wait — actually, the blue angles are:
- One at the top line, on the right side of the transversal
- One at the middle line, on the right side of the transversal

So they are corresponding angles? Yes — because they are in the same relative position (both on the right side, above the transversal) → so they are corresponding angles.

Similarly, the green angles:
- One on the middle line, on the left side of the transversal
- One on the bottom line, on the left side of the transversal
- Both are between the lines? The green angles are inside the lines and on the same side of the transversal → so they are co-interior angles?

Wait — but they are on different pairs.

But co-interior angles are defined for two lines.

But here, the green angles are:
- One on the middle line
- One on the bottom line
- Both on the same side of the transversal
- Both between the lines

So they are co-interior angles.

But are they alternating? No — same side.

Are they corresponding? Only if they are in the same relative position — yes, both are on the left side, and below the transversal? Wait — the transversal is slanting.

Actually, the green angles are on the same side of the transversal and inside the lines → so they are co-interior.

But wait — the blue angles: both on the same side of the transversal and between the lines? Yes — both on the right side, and between the lines.

But are they corresponding?

Yes — because they are in the same relative position (both are "upper-right" angles formed by the transversal and the line) → so they are corresponding angles.

Similarly, the green angles are on the same side (left), and between the lines → so they are co-interior.

Wait — but co-interior requires being on the same side and between the lines — yes.

But in a set of three lines, co-interior can still apply.

So:

✔ Type of angles (blue): Corresponding
✔ Type of angles (green): Co-interior

Wait — but the green angles are not adjacent to the same pair — but they are on the same side of the transversal and between the lines → so yes, they are co-interior.

But let’s double-check.

Alternatively, are the green angles alternate interior? No — they are on the same side.

So final answer:

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✔ Final Answers:

1. Co-interior
2. Alternating
3. Blue: Alternating; Green: Co-interior
4. Blue: Alternating; Green: Corresponding
5. Co-interior
6. Blue: Corresponding; Green: Co-interior

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Summary Table:

| Question | Type of Angles |
|--------|----------------|
| 1 | Co-interior |
| 2 | Alternating |
| 3 | Blue: Alternating; Green: Co-interior |
| 4 | Blue: Alternating; Green: Corresponding |
| 5 | Co-interior |
| 6 | Blue: Corresponding; Green: Co-interior |

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