Anita says the plus sign + forms 2 pairs of vertical angles. Charles says it forms 2 pairs of congruent angles. Who is correct? Explain.
both. vertical angles are congruent.
Anita is correct. The plus sign (+) indeed forms 2 pairs of vertical angles. Vertical angles are the pair of opposite angles formed when two lines intersect. In the case of a plus sign (+), there are two pairs of intersecting lines, each forming a pair of vertical angles.
On the other hand, Charles is incorrect in stating that the plus sign forms 2 pairs of congruent angles. Congruent angles are angles that have the same measure or size. In the case of a plus sign, the angles formed on each side of the intersection are not necessarily congruent. The angles formed by the vertical pairs are equal in measure, but these pairs of angles are not necessarily congruent to each other. Therefore, Anita is correct in saying that the plus sign forms 2 pairs of vertical angles, but Charles is incorrect in saying that it forms 2 pairs of congruent angles.
To determine who is correct, let's first understand the concepts of vertical angles and congruent angles.
1. Vertical angles: Vertical angles are formed when two lines intersect. They are opposite angles that share a common vertex but are not adjacent. Vertical angles are always equal, meaning they have the same measure.
2. Congruent angles: Congruent angles are angles that have the same measure. In other words, their angles are equal.
Now, let's evaluate Anita's statement that the plus sign + forms 2 pairs of vertical angles. To do this, imagine drawing a plus sign on a piece of paper. The horizontal line (—) intersects the vertical line (|) at their common point. This creates four angles: two top angles and two bottom angles.
Looking at these angles, we can see that each pair of top angles is a pair of vertical angles. Similarly, each pair of bottom angles is also a pair of vertical angles. Thus, Anita is correct when she says that the plus sign + forms 2 pairs of vertical angles.
Now, let's examine Charles's claim that the plus sign + forms 2 pairs of congruent angles. By definition, congruent angles have the same measure. However, when we look at the plus sign, we can see that the angles on the top and bottom are not necessarily equal. They may have different measures.
Therefore, Charles is incorrect in stating that the plus sign + forms 2 pairs of congruent angles. While the plus sign does form vertical angles, which are equal, it does not necessarily form congruent angles.
In summary, Anita is correct, while Charles is incorrect. The plus sign + forms 2 pairs of vertical angles, but not 2 pairs of congruent angles.