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The question asks how we know that line \( \overline{AB} \) is perpendicular to \( \overline{CD} \) based on the straightedge and compass construction shown in the diagram. From the options given:

- **Congruency of angles at the intersection**: When two lines intersect and form congruent angles, we can determine whether they are perpendicular if the angles formed are right angles (i.e., 90°).

- **Supplementary and complementary angles**: If two angles sum to 180°, they are supplementary, and if they sum to 90°, they are complementary. For lines to be perpendicular, the angles must sum to 90° (which is the definition of complementary).

The correct answer is **B**:
> **B.** The angles at the intersection of the two lines can be proven to be congruent and complementary, so they meet at a right angle and the lines are perpendicular.

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Here are 5 related questions:
1. How do we prove two lines are perpendicular using only a compass and straightedge?
2. What is the difference between complementary and supplementary angles?
3. Can two lines be perpendicular without forming right angles?
4. How do congruent angles relate to perpendicular lines?
5. What is the role of a straightedge and compass in geometric constructions?

**Tip**: When using a compass and straightedge to prove perpendicularity, you're often creating congruent right angles at the intersection!

In the straightedge and compass construction of the perpendicular line below, how do you know that AB is perpendicular to CD?

Explore how to determine that line AB is perpendicular to line CD in a straightedge and compass construction. Learn about congruent angles, complementary angles, and how to prove perpendicularity using geometric methods. Suitable for students in Grades 8-10.

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