Very simply, geometers examine a pair of rectangles on graph paper and find a translation and rotation to demonstrate their congruence. A couple of questions follow to stimulate critical thinking about other possibilities.

Given the lines of symmetry in an equilateral triangle, your learners find where the pre-image vertices are mapped onto the new image. They explore the properties of equilateral triangles, the impact of reflections, and the...

Young mathematicians investigate the use of symmetry in graphic design. After first learning about reflection, translational, and rotational symmetry, children use this new knowledge to identify symmetry in letters of the...

While it may seem incredibly obvious to the geometry student that congruent sides make congruent triangles, the proving of this by definition actually takes a bit of work. This exercise steps the class through this kind of proof by...

Two triangles are displayed on a coordinate plane. Youngsters apply a reflection and a translation to demonstrate their congruence. This exercise makes a terrific tool for teaching these concepts, or a way to assess learning.

Comparing the movement of graphs geometrically when small changes are made to the parent function motivates this collaborative discussion on the transformations of functions to their various forms. Vertical and horizontal shifts due to...

Reflected waves of light move within a plane, and because of this, polarizing materials can reduce the glare our eyes see. This resource explains how to set up a demonstration of this effect. Consider it for use in your physical science...

The task at hand is to partition a hexagon into two, four, and eight congruent figures. Make sure to give your wizards a sheet of triangle grid paper on which to decompose the hexagons. Have them explain which rotations, reflections, or...

Proving triangles are similar is often an exercise in applying one of the many theorems young geometers memorize, like the AA similarity criteria. But proving that the criteria themselves are valid from basic principles is a great...

Learners investigate the symmetries of a convex quadrilateral in a collaborative activity. Rigid motion and complements are explored as learners analyze different cases of reflections across a line.

Young geometers flex their transformation muscles in this brief but powerful exercise using dilations and translations to develop the similarity of circles. The plan provides guidelines to help learners navigate a pair of...

Geometers prove that triangle PQR is congruent to triangle ABC by describing any combination of rotations, reflections, and translations that would prove it so. There is only this single task on the handout, but a detailed explanation of...

Learners explore mapping a rectangle onto itself using rigid motion concepts, geometric intuition and experimenting with manipulatives in a collaborative task.

Your learners find as many rigid motions of the plane as they can that are symmetries of the configuration of circles. Rigid transformations of the plane are explored and become more concrete to them as they visualize and execute...

Learners examine the properties of quadrilaterals from the point of view of rigid motion. Different types of quadrilaterals are characterized by their symmetries, so learners explore the symmetries of a described quadrilateral to...

Use the handout as guided or independent practice in drawing a reflection of a rectangle over a line. Three rectangles are provided for practice in addition to a critical thinking question.

In this activity, students will investigate the relationship among the three types of rigid transformations - translations, rotations, and reflections.

This site is a Geometer's Sketch Pad lesson plan where students explore tessellations through reflections, rotations, and translations.

An introductory look at the interactive Geometer's Sketchpad in terms of using it to explore rotations, translations, and reflections. Only a beginner's amount of skill with the program is needed. Exploration questions are given for the...

Students move their cursor in this activity center to occupy a unique point on a background letter "F" in quadrant 1. Students then together follow a rule for going to a different point (such as "use the opposite of the original x...

In this activity, students describe how to move a shape from one place to another in a plane. They learn about translations, rotations, and line reflections. [Requires Adobe Reader.]

This site presents information on the three basic transformations of figures in a plane: Reflections, Rotations, and Translations.

What lowercase letters read the same both upside down and right side up? If you have the answer, then you can handle this geometric symmetry math challenge. A one-page activity from the NTCM Math Challenge for Families collection....

Find a quick, concise explanation of the transformations of graphs: translations, reflections and rotations. Examples are given and clearly explained for each transformation.