- Vertical angles are opposite angles created by two intersecting lines.
- Vertical angles are always congruent (have the same measure).
- Choice (c) correctly identifies that vertical angles are opposite and congruent.
- Final answer is \(\boxed{c}\).
Explanation
- Definition of vertical angles
Vertical angles are defined in geometry as the pair of non-adjacent angles formed by the intersection of two straight lines. These angles lie opposite each other at the vertex where the lines cross. A fundamental property of vertical angles, known as the Vertical Angles Theorem, is that they are always congruent, meaning they have the same measure.
- Evaluating the options
We analyze the given choices based on the definition:
- (a) Two angles that share a common side: This describes adjacent angles, not vertical angles.
- (b) Two angles having measures that sum to 90 degrees: This is the definition of complementary angles.
- (c) Opposite, congruent angles formed when two lines intersect: This matches the geometric definition and property of vertical angles.
- (d) Two angles having measures that sum to 180 degrees: This is the definition of supplementary angles.
- (e) None of the above: Since (c) is a correct definition, this option is incorrect.
Thus, the correct choice is (c).
Examples
Imagine you are looking at a pair of scissors partially open. The two blades form a set of intersecting lines. The angle formed at the tip between the two blades pointing towards the top, and the angle formed at the tip between the two blades pointing towards the bottom, are vertical angles. Because they are vertical angles, you can be certain that no matter how much you open or close the scissors, these two angles will always remain exactly equal in size. This property is frequently used in construction and design to ensure symmetry and balance.