Home
Back
Vertical Angles Principle:
When two lines intersect, the angles opposite each other (vertical angles) are equal.
| From: | To: |
Vertical angles are the angles opposite each other when two lines intersect. They are always congruent (equal in measure). The two angles adjacent to any vertical angle are supplementary (add up to 180°).
The Vertical Angles Theorem states:
When two lines intersect, they form two pairs of vertical angles that are equal.
Key Properties:
Applications: Vertical angles are used in architecture, engineering, navigation, and various geometric proofs. They help solve problems involving intersecting lines and angle relationships.
Instructions: Simply enter the measure of one angle (between 0° and 360°) and the calculator will show the measure of its vertical angle.
Q1: Are vertical angles always congruent?
A: Yes, vertical angles formed by two intersecting lines are always equal in measure.
Q2: Can vertical angles be right angles?
A: Yes, if two lines intersect at right angles, all four angles formed will be 90°.
Q3: How are vertical angles different from adjacent angles?
A: Vertical angles are opposite each other and equal, while adjacent angles share a common side and are supplementary.
Q4: Do vertical angles have to be up and down?
A: No, the "vertical" refers to their position relative to each other, not their orientation in space.
Q5: Can vertical angles exist with more than two lines?
A: Vertical angles are specifically formed by two intersecting lines. With more lines, the relationships become more complex.