The goal of this task is to understand how congruence of triangles, defined in terms of rigid motions, relates to the corresponding sides and angles of triangles. Aligns with G-CO.B.7.

Given an equilateral triangle, students are asked to explore its symmetries using rigid transformations of the plane. Aligns with G-CO.B.

Given distinct, congruent triangles, students are asked to show that congruence can always be shown with one, two, or three rigid motions. Aligns with G-CO.A.5.

The goal of this task is to use the unit circle and rigid transformations in order to establish some fundamental trigonometric function identities. Aligns with F-TF.A.2 and F-TF.A.4.

Roman society was rigidly structured by wealth and rank, through both of which equestrians could increase their status. Even the plebs became class-divided. Augustus enabled the municipalities of Italy to practice local government....

Chitin is a biopolymer that gives rigidity to exoskeletons and other protective structures of organisms, thereby preventing injury to soft internal tissues and other parts. Its chemical structure is shown and its functions are described.

This task examines the rigid motions which map a rectangle onto itself. The emphasis here is on careful reasoning using the definitions of reflections and rotations. Aligns with G-CO.A.3.

In this task, students must show that two triangles are congruent given a set of steps which produce a rigid transformation of the plane. Includes an experimental GeoGebra worksheet that instructors can use to demonstrate the task....

This is an image of a crowned and bejeweled Buddha, standing on a lotus pedestal, surrounded by four other figures representing four famous scenes from the life of the historical Buddha. It dates from approximately 1050-1100 C.E. The...

Learn how similarity transformation is one or more rigid transformations (reflection, rotation, translation) followed by a dilation.

Understand the rigid transformation of a rotation.

Explore the rigid transformations of shape reflections.

[Free Registration/Login may be required to access all resource tools.] In this lesson, students learn how to translate a figure. They examine guided notes, review examples, watch instructional videos, and try practice problems.

A video lesson that introduces the components of circular motion. Understand that any objects that rotates around a point is in circular motion. Video also explores how to measure how far an object has rotated. Video gives equation for...

Explores how to predict degrees of freedom of a mechanism. Understand that in mechanics degrees of freedom is one of the most important concepts. Video length: 4 min. 41 sec.

This lesson focuses on wallpaper groups. While there are infinitely many possible patterns, they all have one of just 17 different symmetry groups. These are called the Wallpaper Groups. Every wallpaper group is defined by a combination...

This task applies reflections to a regular hexagon to construct a pattern of six hexagons enclosing a seventh. The focus of the task is on using the properties of reflections to deduce this seven-hexagon pattern. Aligns with G-CO.B.6.

This task applies reflections to a regular octagon to construct a pattern of four octagons enclosing a quadrilateral. The focus of the task is on using the properties of reflections to deduce that the quadrilateral is actually a square....

In this task, students are shown three unit squares and two line segments connecting two pairs of vertices. They are asked to find the area of a triangle formed by intersecting lines. They can solve it using coordinate geometry or...

For this task, students are given four sets of coordinate pairs and are asked to determine if they represent a rectangle. Aligns with 8.G.A, 8.G.B, G-CO.B, G-GPE.B, and G-SRT.B.5.

Eighth graders are presented with a labeled drawing of two parallel lines intersected by a transversal line. They are asked to discuss congruency of angles when the picture is rotated about a point on the transversal. Aligns with 8.G.A.5.

[Free Registration/Login may be required to access all resource tools.] Reflect a figure.

[Free Registration/Login may be required to access all resource tools.] This concept introduces geometric rotations.

[Free Registration/Login may be required to access all resource tools.] This concept teaches students to compose transformations and how to represent the composition of transformations as a rule. Students examine guided notes, review...