congruent figures
two or more figures with the same sides and angles
Congruent figures refer to two or more plane figures that have the same size and shape. In mathematics, we use the term congruent to describe these figures. Two figures are congruent if they can be transformed into each other by a series of rigid motions, such as translation, rotation, and reflection. This means that the lengths of their corresponding sides are equal and their corresponding angles are congruent.
For example, two triangles are congruent if their corresponding sides and angles are equal. That is, if all three sides and three angles of one triangle are equal to those of another, then they are congruent. We use the symbol ≅ to show congruence. Thus, if triangle ABC is congruent to triangle DEF, we write it as ΔABC ≅ ΔDEF.
Congruent figures are important in many areas of geometry, such as in proving theorems and solving real-world problems. For example, congruent triangles can be used to find the height of a building or the width of a river, as long as the similar triangles have corresponding congruent sides.
It is also important to note that if two figures are not congruent, they may still be similar. Similar figures have the same shape but different sizes. In this case, the corresponding angles are congruent, but the corresponding sides are proportional rather than equal.
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