This task is intended for instruction, providing the students with a chance to experiment with physical models of triangles, gaining spatial intuition by executing reflections.

In this three-lesson unit, students participate in activities in which they focus on connections between mathematics and children’s literature. Three pieces of literature are used to teach geometry and measurement topics in the mathematics curriculum, i.e. using and describing geometric figures, estimating the volume of an irregular solid, and exploring the need for a standard unit of length. Activity worksheets and ideas for extension are included.

(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.)

Así como se utilizan movimientos rígidos para definir la congruencia en el Módulo 1, se agregan dilataciones para definir la similitud en el Módulo 2. Para poder discutir la similitud, los estudiantes primero deben comprender claramente cómo se comportan las dilataciones. Esto se hace en dos partes, al estudiar cómo las dilataciones producen dibujos de escala y razonando por qué las propiedades de las dilataciones deben ser ciertas. Una vez que las dilataciones se establecen claramente, se definen transformaciones de similitud y se examinan las relaciones de longitud y ángulo, lo que produce criterios de similitud triangular. Sigue una mirada profunda a la similitud dentro de los triángulos rectos, y finalmente el módulo termina con un estudio de trigonometría del triángulo recto.

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

English Description:
Just as rigid motions are used to define congruence in Module 1, so dilations are added to define similarity in Module 2.  To be able to discuss similarity, students must first have a clear understanding of how dilations behave.  This is done in two parts, by studying how dilations yield scale drawings and reasoning why the properties of dilations must be true. Once dilations are clearly established, similarity transformations are defined and length and angle relationships are examined, yielding triangle similarity criteria.  An in-depth look at similarity within right triangles follows, and finally the module ends with a study of right triangle trigonometry.

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

In this unit, students investigate fractional parts of the whole and use translations, reflections, rotations, and line symmetry to make four-part quilt squares. Students have a practical context for using the mathematical terms associated with divisions of the square, transformations, and symmetries. Suggestions for implementation and extensions are included.

This interactive applet lets students create quilting type patterns and explore tessellation possibilities. The applet gives learners a choice of six polygons that can be turned or flipped and fitted together. Suggestions for exploration and five challenge patterns are provided. The tool supports a number of lessons and units including What's So Special About Triangles and Virtual Pattern Blocks (cataloged separately).

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.

The result here complements the fact, presented in the task ``Right triangles inscribed in circles I,'' that any triangle inscribed in a circle with one side being a diameter of the circle is a right triangle. A second common proof of this result rotates the triangle by 180 degrees about M and then shows that the quadrilateral, obtained by taking the union of these two triangles, is a rectangle.

This is the first version of a task asking students to find the areas of triangles that have the same base and height, and is the most concrete.

This is the second version of a task asking students to find the areas of triangles that have the same base and height. This presentation is more abstract as students are not using physical models.

In this web-based application from Illuminations students must sort shapes based on the categories of the Venn diagram. Users can choose the categories from a drop down menu. The application includes instructions and exploration steps.

This interactive tool allows a user to create many geometric shapes. Squares, triangles, rhombi, trapezoids and hexagons can be created, colored, enlarged, shrunk, rotated, reflected, sliced, and glued together.

This lesson unit is intended to help teachers assess how well students are able to identify and use geometrical knowledge to solve a problem. In particular, this unit aims to identify and help students who have difficulty in: making a mathematical model of a geometrical situation; drawing diagrams to help with solving a problem; identifying similar triangles and using their properties to solve problems; and tracking and reviewing strategic decisions when problem-solving.

In this video segment adapted from ZOOM, the cast tries to design and build a bridge made out of drinking straws that will support the weight of 200 pennies.

In this activity, learners walk the sides and interior angles of various polygons drawn on the playground. As they do so, learners practice rotating clockwise 180 and 360 degrees. Learners discover there is a pattern to the sum of the interior angles of any polygon.

In this geometry lesson students classify triangles and explore side lengths of triangles to discover the Triangle Inequality Theorem. The resource includes an exploratory activity and student sheet (pdf), class discussion prompts, a small group spinner activity, extension suggestions, and links to two related resources (cataloged separately).

I use this activity to reinforce the vocabulary used when practicing with polygons.  Students are asked to describe a polygon by identifying what it is, but also what it is NOT. 

In these two geometry activities students explore the properties of triangles, discover what shapes triangles can form, and investigate what shapes can form triangles. Each activity includes a student recording sheet, extension ideas, and questions for students. Cataloged separateley within this site are the Patch Tool and the related How Many Triangles Can You Construct? activity.

The triangle congruence criteria, SSS, SAS, ASA, all require three pieces of information. It is interesting, however, that not all three pieces of information about sides and angles are sufficient to determine a triangle up to congruence. In this problem, we considered SSA. Also insufficient is AAA, which determines a triangle up to similarity. Unlike SSA, AAS is sufficient because two pairs of congruent angles force the third pair of angles to also be congruent.