Una aserción es una afirmación que alguien cree que es verdadera, pero que todavía no se ha demostrado.
Dos figuras son congruentes si existe un movimiento rígido o una secuencia de movimientos rígidos (traslaciones, rotaciones y reflexiones) que lleva una figura a la otra.
En esta figura, el triángulo A es congruente al triángulo D.
Una traslación lleva el triángulo A al triángulo B.
Una rotación lleva el triángulo B al triángulo C.
Una reflexión lleva el triángulo C al triángulo D.
Una imagen es el resultado de una transformación. Todas las partes de la figura original son llevadas de la misma manera y cada parte corresponde a una parte de la imagen.
Este diagrama muestra una transformación que lleva a .
es el original y es la imagen.
Una transformación rígida es un movimiento que no cambia ninguna de las medidas de una figura.
Las traslaciones, rotaciones y reflexiones son movimientos rígidos y cualquier secuencia de ellos es una transformación rígida.
Standards Alignment
Building On
8.G.A.2
Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them.
Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). Copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line.
Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch).
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.
Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch).
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.
Prove theorems about triangles. Theorems include: measures of interior angles of a triangle sum to ; base angles of isosceles triangles are congruent; the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; the medians of a triangle meet at a point.
Prove theorems about lines and angles. Theorems include: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent; points on a perpendicular bisector of a line segment are exactly those equidistant from the segment's endpoints.