Parallel and perpendicular lines - riderdop - Free Printable

It looks like you've uploaded a worksheet that includes a diagram with labeled lines and a list of statements about the relationships between these lines (parallel, perpendicular, intersecting). However, based on your request, it seems you want me to solve the problem and explain the solution, but the image itself appears to already contain the answers.

Let’s go through this carefully:

---

🔍 Understanding the Diagram

We have several lines labeled with points:

- AB: A horizontal line going left to right.
- CD: Another horizontal line below AB, also left to right.
- IJ: A vertical line from I (top) to J (bottom), passing through AB and CD.
- GH: Another vertical line from G (top) to H (bottom), passing through AB and CD.
- EF: A diagonal line from E (top-right) to F (bottom-left), crossing AB, CD, IJ, and GH.

There are right-angle symbols (□) at intersections:
- At point A: where IJ meets AB → so IJ ⊥ AB
- At point C: where IJ meets CD → so IJ ⊥ CD
- At point G: where GH meets AB → so GH ⊥ AB
- At point H: where GH meets CD → so GH ⊥ CD

So we can infer:
- IJ is perpendicular to both AB and CD
- GH is perpendicular to both AB and CD
- Since AB and CD are both horizontal and parallel to each other, and both are perpendicular to IJ and GH, then IJ and GH are vertical and parallel to each other.
- EF is a diagonal line that crosses AB, CD, IJ, and GH — so it intersects all of them.

---

✔ Now Let's Evaluate Each Statement

We'll check whether each statement is true or false based on the diagram.

---

#### Left Column:

1. AB and CD are parallel lines
✔ True – Both are horizontal and never meet; they’re equidistant.

2. GH and AB are perpendicular lines
✔ True – Right angle symbol at G shows GH ⊥ AB.

3. AB and EF are intersecting lines
✔ True – They cross at point E (on AB).

4. IJ and AB are perpendicular lines
✔ True – Right angle at A confirms IJ ⊥ AB.

5. GH and IJ are parallel lines
✔ True – Both are vertical, and since they're both perpendicular to the same horizontal lines (AB and CD), they must be parallel.

---

#### Right Column:

6. IJ and CD are perpendicular lines
✔ True – Right angle at C shows IJ ⊥ CD.

7. EF and GH are intersecting lines
✔ True – EF crosses GH somewhere between G and H.

8. GH and CD are perpendicular lines
✔ True – Right angle at H shows GH ⊥ CD.

9. EF and IJ are intersecting lines
✔ True – EF crosses IJ somewhere between I and J.

10. EF and CD are intersecting lines
✔ True – EF crosses CD at some point between C and D.

---

🟩 Final Answer: All Statements Are True

All 10 statements listed in the worksheet are correct based on the diagram.

---

✔ Explanation Summary

- Parallel lines: Lines that never meet and are always the same distance apart.
→ AB ∥ CD, and GH ∥ IJ (both vertical)

- Perpendicular lines: Lines that meet at 90° angles (indicated by square corners).
→ AB ⊥ GH, AB ⊥ IJ, CD ⊥ GH, CD ⊥ IJ

- Intersecting lines: Lines that cross at any angle (not necessarily 90°).
→ EF intersects AB, CD, GH, and IJ

---

✔ Conclusion:

The worksheet has already provided the correct answers. All the statements are accurate based on the geometric relationships shown in the diagram.

> Answer: All statements are true. The diagram correctly shows:
> - AB ∥ CD
> - GH ∥ IJ
> - AB ⊥ GH, AB ⊥ IJ, CD ⊥ GH, CD ⊥ IJ
> - EF intersects AB, CD, GH, and IJ

Let me know if you'd like this turned into a printable explanation or need help with similar problems!