Vertical angles must: Check all that apply. A. be congruent. B. be adjacent. C. have the same vertex. D. be obtuse.
The Correct Answer and Explanation is:
The correct answers are:
A. be congruent.
C. have the same vertex.
Explanation:
Vertical angles are a pair of angles that are formed when two lines intersect. These angles have specific properties, which are central to understanding geometric relationships.
- Congruence of Vertical Angles (A):
One of the fundamental properties of vertical angles is that they are always congruent. This means that if two lines intersect, the opposite (or “vertical”) angles formed by the intersection are equal in measure. For example, if one of the angles is 45 degrees, the vertical angle directly across from it will also measure 45 degrees. This is a direct result of the way the angles are created and is a key geometric property. - Same Vertex (C):
Vertical angles must share the same vertex. This is because they are formed at the point where two lines intersect. The vertex is the point where the lines meet, and the angles that are formed opposite each other must have this common point. Without this shared vertex, the angles would not be classified as vertical angles. - Not Adjacent (B):
Vertical angles are not adjacent to each other. Adjacent angles are those that share a common side, but vertical angles are formed on opposite sides of the intersection and do not share a common side. Thus, they are not adjacent, even though they share the same vertex. - Not Necessarily Obtuse (D):
Vertical angles can be any type of angle (acute, right, or obtuse). There is no requirement for vertical angles to be obtuse. The measure of vertical angles depends on the angles created by the intersecting lines. If the lines intersect at an acute angle, the vertical angles will also be acute, and if the lines form a right angle, the vertical angles will be right angles. Therefore, vertical angles do not have to be obtuse.
In summary, vertical angles must be congruent and have the same vertex, but they do not need to be adjacent or obtuse.
