Anita says that a Plus sign + forms 2 pairs of veritcal angles Charles says it forms 2 pairs of congruent angles who is correct? explain
Both.
http://www.mathopenref.com/anglesvertical.html
http://drdavespsychologypage.intuitwebsites.com/Decision_Trap.pdf
they both are becuz the plus sign forms vertical angles and vertical angles always congruent.
To determine who is correct, we need to understand the definitions of both vertical angles and congruent angles.
Vertical angles are formed when two lines intersect. In this case, Anita claims that a plus sign + forms two pairs of vertical angles. But does it?
To confirm Anita's statement, we can draw a simple schematic of a plus sign +:
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--+--
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By examining the diagram, we can see that indeed, two pairs of vertical angles are formed. Each of the four angles (marked by the + shape) is adjacent to two of the other angles, forming two pairs.
Next, let's discuss congruent angles. Two angles are considered congruent if they have the same measure. Charles claims that the plus sign + forms two pairs of congruent angles. But is he correct?
To verify Charles' claim, we need to determine whether the angles formed by the plus sign + are all congruent. To do this, we can measure the angles and compare their measures. However, since we are considering a schematic representation rather than an actual geometric object, we cannot precisely measure the angles. Therefore, we cannot definitively determine if Charles is correct.
However, if we assume that the plus sign + is symmetric and formed by perpendicular lines, we can infer that the angles are congruent. Because perpendicular lines create right angles, and right angles have a measure of exactly 90 degrees, each pair of angles would indeed be congruent.
So, in conclusion, Anita is correct in saying that the plus sign + forms two pairs of vertical angles. Charles is also correct if we assume that the plus sign + is symmetric and formed by perpendicular lines, as it would then form two pairs of congruent (90-degree) angles.