Parallel and Perpendicular Lines Worksheets - Free Printable

Since I can't view or access uploaded images directly, I can't see the specific diagrams in your image. However, based on the text you provided:

> "Parallel and Perpendicular Lines"
> Determine whether each pair of lines is parallel or perpendicular.

And the mention of multiple diagrams (labeled a, b, c, d), I can guide you through how to solve this type of problem and explain the logic.

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🔍 How to Determine if Two Lines Are Parallel or Perpendicular

#### ✔ Step 1: Understand the Definitions
- Parallel lines: Lines that never intersect and have the same slope.
- Perpendicular lines: Lines that intersect at a 90° angle. Their slopes are negative reciprocals of each other (i.e., if one slope is $ m $, the other is $ -\frac{1}{m} $).

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🧩 How to Analyze Each Diagram

Even without seeing the image, here’s how you would approach each diagram:

#### 🔹 For each pair of lines:
1. Look at their direction:
- If both lines go in the same direction (e.g., both horizontal, both vertical, or both slanting up to the right), they might be parallel.
- If one line goes up and the other goes down at a right angle, they may be perpendicular.

2. Check angles:
- If the lines cross and form a square corner (right angle), they are perpendicular.
- If they never meet and maintain equal distance, they are parallel.

3. Use slope concepts (if coordinates are given):
- Calculate the slope of each line using two points:
$$
\text{slope} = \frac{y_2 - y_1}{x_2 - x_1}
$$
- Compare slopes:
- Same slope → parallel
- Product of slopes = $-1$ → perpendicular

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📌 Common Cases (Based on Typical Problems)

Let’s assume the four diagrams look like this (common textbook examples):

#### a) Two diagonal lines crossing at an angle
- If they form a "cross" but not at 90° → neither parallel nor perpendicular
- But if they form a right angle → perpendicular

#### b) One horizontal line, one vertical line
- These always intersect at 90° → perpendicular

#### c) Two diagonal lines going in the same direction
- Same slope → parallel

#### d) Two vertical lines
- Both go straight up/down → same slope (undefined) → parallel

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✔ Example Answers (Typical Case)

Assuming standard configurations:

| Diagram | Relationship |
|--------|--------------|
| a | Perpendicular (forms right angle) |
| b | Perpendicular (horizontal & vertical) |
| c | Parallel (same direction) |
| d | Parallel (both vertical) |

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💡 Final Tip

If you can describe the diagrams (e.g., “one line is horizontal, another is vertical”, or “two lines slanting upward at the same angle”), I can give you exact answers!

Alternatively, if you can extract the coordinates from the image, I can calculate slopes for you.

Would you like to describe the diagrams?