One student says “My sister’s high school geometry book talked about equal angles. Why don’t we use the term equal angels instead of congruent angles? How do you reply?
When the student asks why we don't use the term "equal angles" instead of "congruent angles," you can provide the following response:
The terms "equal angles" and "congruent angles" are essentially used interchangeably in mathematics. They both refer to angles that have the same measurement or size. While "equal angles" is a more general description, the term "congruent angles" is more commonly used in geometry.
To explain further, "congruent" is a mathematical term that means two geometric figures are exactly the same size and shape. In the case of angles, when we say that two angles are congruent, it implies that their measurements are the same. This concept is primarily used in geometry to describe relationships between different angles in geometric shapes.
In contrast, "equal" is a more general term that can be used in various mathematical contexts. For example, we use "equal" to describe the equivalence of numbers, lengths, or values. However, in geometry, the term "congruent" is more specific and commonly used to describe the equality of angles.
Therefore, while using the term "equal angles" may be technically correct, it is more typical in geometry to use the term "congruent angles" to specifically refer to angles with the same measurement.