Question 2 10 2 Points Vertical angles must: Check all that apply. A. be obtuse. B. have the same vertex. C. be congruent. D. be adjacent.
The Correct Answer and Explanation is:
B. have the same vertex.
This statement is correct. The point where the two lines cross isThe correct answers are B. have the same vertex called the vertex. All four angles created by this intersection share this single point as their vertex. By definition, a pair of vertical angles and C. be congruent.
Here is an explanation of why these options are correct and the others are incorrect. is located at this intersection, so they must share the same vertex. This is an essential part of what makes them vertical angles.
Vertical angles are a specific pair of angles formed when two straight lines intersect. Imagine two lines crossing to form an “X” shape. The angles that are directly opposite each other in this “X” are vertical angles. For example, the angle at the top is vertical to the angle at the bottom, and the angle on the left is vertical to the angle onC. be congruent.
This statement is also correct. “Congruent” is a geometric term meaning the the right.
B. have the same vertex. This statement is correct. The very definition of vertical angles requires angles have the exact same measure. The Vertical Angles Theorem proves that vertical angles are always congruent. This is because any angle in them to be formed by two intersecting lines. The single point where these two lines cross is called the vertex. Since both angles in a vertical pair are formed at this intersection point, they necessarily share that same vertex. It is the central point that connects them the intersection forms a linear pair with its adjacent angles, meaning they add up to 180 degrees. Since a pair of vertical.
C. be congruent. This statement is also correct and is a fundamental theorem in geometry. Congruent means that angles are both supplementary to the same adjacent angle, they must be equal to each other. For instance, if angle 1 the angles have the same measure. Vertical angles are always equal to each other. This can be proven by observing that the and angle 2 are adjacent and sum to 180 degrees, and angle 2 and angle 3 are also adjacent adjacent angles in the “X” formation are supplementary, meaning they add up to 180 degrees because they form a straight and sum to 180 degrees, it logically follows that angle 1 and angle 3 must be equal.
Now, let’s examine the incorrect options.
A. be obtuse.
This statement is incorrect. An line. If one angle is, for instance, 110 degrees, the angle adjacent to it must be 70 obtuse angle is one that measures more than 90 degrees. While some vertical angles are obtuse, this is not a mandatory degrees (180 – 110 = 70). The angle vertical to the original 11 characteristic. For example, if two lines intersect perpendicularly, they form four 90 degree right angles. In this case, the0-degree angle is also adjacent to that same 70-degree angle, so it too must be 1 vertical angles are right angles, not obtuse. If the lines intersect at a different slant, one pair of vertical angles will be10 degrees. This logic holds for any pair of intersecting lines, proving that vertical angles are always congruent.
**A. be acute (less than 90 degrees). Therefore, vertical angles are not always obtuse.
D. be adjacent.
obtuse.** This is incorrect. An obtuse angle is greater than 90 degrees. While a pair of vertical angles can be obtuse,This statement is incorrect. Adjacent angles are angles that share a common vertex and a common side, but do not overlap. Vertical they do not have to be. If two lines intersect to form an acute angle (less than 90 degrees), angles share a vertex, but they are on opposite sides of that vertex and do not share a side. They are defined like 50 degrees, its vertical angle will also be 50 degrees. If two lines are perpendicular, all four angles formed by their non-adjacent, opposite positions. will be 90-degree right angles. Vertical angles can be acute, right, or obtuse.
D. be adjacent. This is incorrect. Adjacent angles are angles that share a common vertex and a common side. Vertical angles share a vertex but are on opposite sides of it; they do not share a common side. In fact, they are defined as non-adjacent angles.
