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why can't they just say two angles are equal instead of congruent? when is it acceptable to just say two things are equal to each other?
mezarashi said:As far as I know, if two angles are congruent, they are equal. But if two triangles are congruent, they are not necessarily equal. If they are equal, they must be congruent however. The definition here would be, equal in relative dimensions but different in scale.
Congruent and equal are two terms used to describe relationships between geometric shapes or figures. While these terms are often used interchangeably, there are subtle differences between them.
Both congruent and equal describe a relationship where two geometric shapes or figures have the same size or measure. They indicate that the shapes or figures are identical in shape and size.
Two shapes are congruent if they have the same shape and size, but may be oriented differently or have different positions in space. In other words, they can be transformed into each other through a combination of rotations, reflections, and translations.
Two shapes are equal if they have the same shape, size, and orientation. This means that they are essentially identical and cannot be transformed into each other through any combination of rotations, reflections, and translations.
Congruent and equal are important concepts in geometry and are used to define relationships between geometric shapes or figures. They are also used to prove geometric theorems and solve problems related to angles, sides, and other measurements of shapes.