The activities in this four-lesson unit enable students to use their knowledge of number, measurement, and geometry to solve interesting problems. Planning and visualizing, estimating and measuring, and testing and revising are components of the ladybug activities. Students design "virtual paths" that enable a ladybug to either hide under a leaf or go through a maze. They develop navigational skills by testing their path and revising it. Two interactive Java applets (Ladybug Mazes and Hiding Ladybug, cataloged separately) support student solutions.

This 3 lesson instructional unit helps students investigate many different aspects of triangles including basic properties of triangles, building other shapes from triangles, the dependence of the third side length on the other two (Triangle Inequality Theorem), and the Sierpinski Triangle fractal. The lesson includes student activity sheets and links to interactive applets.

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.

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 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.

In this primary grades Illuminations lesson, students identify figures on a football field. They look for both congruent and similar figures, and they consider figures that are the same but that occur in a different orientation because of translation, rotation, or reflection. The lesson includes a student worksheet and discussion questions.

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.

This familiar game can be played by one or two players taking turns. Players choose to match equivalent representations of numbers, shapes, fractions, or multiplication facts. The game can be played in clear pane mode, or for added challenge, with the windows closed.

This activity has students explore the patterns that emerge when connecting midpoints of triangles. The activity includes a student worksheet, discussion questions, and an interactive fractal tool.

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.

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.

This problem introduces the circumcenter of a triangle and shows how it can be used to inscribe the triangle in a circle. It also shows that there cannot be more than one circumcenter.

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).

The purpose of this task is to help students understand what is meant by a base and its corresponding height in a triangle and to be able to correctly identify all three base-height pairs.

This task shows that the three perpendicular bisectors of the sides of a triangle all meet in a point, using the characterization of the perpendicular bisector of a line segment as the set of points equidistant from the two ends of the segment. The point so constructed is called the circumcenter of the triangle.

This task focuses on a remarkable fact which comes out of the construction of the inscribed circle in a triangle: the angle bisectors of the three angles of triangle ABC all meet in a point.

For these particular triangles, three reflections were necessary to express how to move from ABC to DEF. Sometimes, however, one reflection or two reflections will suffice. Since any rigid motion will take triangle ABC to a congruent triangle DEF, this shows the remarkable fact that any rigid motion of the plane can be expressed as one reflection, a composition of two reflections, or a composition of three reflections.

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.

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.

(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.