Las partes correspondientes son las partes que están en las mismas posiciones relativas de una figura original y su copia a escala. Las partes pueden ser puntos, segmentos, ángulos o distancias. Cuando dos figuras son congruentes, todas sus partes correspondientes son congruentes.
Por ejemplo, en los triángulos y :
El punto corresponde al punto .
El segmento corresponde al segmento .
El ángulo corresponde al ángulo .
Standards Alignment
Building On
8.G.A.1
Verify experimentally the properties of rotations, reflections, and translations:
Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. For example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so.
Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another.
Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent.
Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent.
Prove theorems about parallelograms. Theorems include: opposite sides are congruent, opposite angles are congruent, the diagonals of a parallelogram bisect each other, and conversely, rectangles are parallelograms with congruent diagonals.
