This lesson unit is intended to help teachers assess how well students are able to: work with concepts of congruency and similarity, including identifying corresponding sides and corresponding angles within and between triangles; Identify and understand the significance of a counter-example; Prove, and evaluate proofs in a geometric context.

The purpose of this task is primarily assessment-oriented, asking students to demonstrate knowledge of how to determine the congruency of triangles.

This is a task from the Illustrative Mathematics website that is one part of a complete illustration of the standard to which it is aligned. Each task has at least one solution and some commentary that addresses important asects of the task and its potential use. Here are the first few lines of the commentary for this task: Below is a picture of two triangles: Suppose there is a sequence of rigid motions which maps $\triangle ABC$ to $\triangle DEF$. Explain why correspond...

Module 1 embodies critical changes in Geometry as outlined by the Common Core. The heart of the module is the study of transformations and the role transformations play in defining congruence. The topic of transformations is introduced in a primarily experiential manner in Grade 8 and is formalized in Grade 10 with the use of precise language. The need for clear use of language is emphasized through vocabulary, the process of writing steps to perform constructions, and ultimately as part of the proof-writing process.

Find the rest of the EngageNY Mathematics resources at https://archive.org/details/engageny-mathematics.

(Nota: Esta es una traducción de un recurso educativo abierto creado por el Departamento de Educación del Estado de Nueva York (NYSED) como parte del proyecto "EngageNY" en 2013. Aunque el recurso real fue traducido por personas, la siguiente descripción se tradujo del inglés original usando Google Translate para ayudar a los usuarios potenciales a decidir si se adapta a sus necesidades y puede contener errores gramaticales o lingüísticos. La descripción original en inglés también se proporciona a continuación.)

El módulo 1 incorpora cambios críticos en la geometría según lo descrito por el núcleo común. El corazón del módulo es el estudio de las transformaciones y el papel que juegan las transformaciones para definir la congruencia. El tema de las transformaciones se introduce de manera principalmente experiencial en el grado 8 y se formaliza en el grado 10 con el uso de un lenguaje preciso. La necesidad de un uso claro del lenguaje se enfatiza a través del vocabulario, el proceso de escribir pasos para realizar construcciones y, en última instancia, como parte del proceso de escritura de prueba.

Encuentre el resto de los recursos matemáticos de Engageny en https://archive.org/details/engageny-mathematics.

English Description:
Module 1 embodies critical changes in Geometry as outlined by the Common Core. The heart of the module is the study of transformations and the role transformations play in defining congruence. The topic of transformations is introduced in a primarily experiential manner in Grade 8 and is formalized in Grade 10 with the use of precise language. The need for clear use of language is emphasized through vocabulary, the process of writing steps to perform constructions, and ultimately as part of the proof-writing process.

Find the rest of the EngageNY Mathematics resources at https://archive.org/details/engageny-mathematics.

This activity is one in a series of tasks using rigid transformations of the plane to explore symmetries of classes of triangles, with this task in particular focusing on the class of equilaterial triangles. In particular, the task has students link their intuitive notions of symmetries of a triangle with statements proving that the said triangle is unmoved by applying certain rigid transformations.

This task examines some of the properties of reflections of the plane which preserve an equilateral triangle: these were introduced in ''Reflections and Isosceles Triangles'' and ''Reflection and Equilateral Triangles I''. The task gives students a chance to see the impact of these reflections on an explicit object and to see that the reflections do not always commute.

This activity is one in a series of tasks using rigid transformations of the plane to explore symmetries of classes of triangles, with this task in particular focussing on the class of isosceles triangles.