Verify experimentally the properties of rotations, reflections, and translations:
Official wording from the Common Core State Standards for Mathematics (© 2010 National Governors Association Center for Best Practices and Council of Chief State School Officers). View on thecorestandards.org
Slide a shape across a page, flip it over a line, or turn it around a point, and something stays the same: its size and shape. These three moves, translations, reflections and rotations, are called rigid transformations. Eighth graders verify their properties by experiment, using tracing paper, transparencies or geometry apps, rather than taking them on trust.
Three facts are checked directly. Lines are taken to lines and segments to segments of the same length, so a side 5 cm long stays 5 cm. Angles are taken to angles with the same measure, so a 70° angle remains 70°. Parallel lines stay parallel. What can change is position and orientation: a reflection reverses the order of vertices (clockwise becomes counterclockwise) and a rotation turns the figure. Knowing exactly what is preserved is the foundation for defining congruence in 8.G.A.2. Students who can say which features survive each move, and why, are ready to describe a whole chain of moves later.
A figure turned 90° can look smaller when drawn on a slant. Measuring the sides shows they are unchanged.
A reflected triangle ABC labelled clockwise becomes counterclockwise. Students should check the order of the labels, not only the shape.
In a translation every point moves the same distance in the same direction. Moving one corner further than another distorts the shape.
Dilations change lengths, so they are not rigid. They come into play in 8.G.A.3 and 8.G.A.4 with similarity.
Segment AB has endpoints A(1, 2) and B(4, 6). Reflect it over the y-axis and check that its length is unchanged.
Answer: A'(-1, 2), B'(-4, 6); both segments have length 5.
Tracing paper is the classic tool: students trace a figure, apply a move, and lay the tracing over the image to compare. Ask them to record measurements before and after in a table so the evidence is explicit. Geometry software makes it easy to drag figures and watch lengths and angles stay fixed.
On assessments, expect questions asking which property is preserved, or which statement about an image is true. Encourage precise vocabulary: image, pre-image, prime notation (A'), and the words translation, reflection and rotation rather than slide, flip and turn.
Original questions written for this standard. Choose an option or type your answer, then press Check. Every question has a worked explanation.
Answer: D) 6 units
Rotations preserve lengths, so P'Q' is also 6 units.
Answer: A) Orientation (clockwise order of vertices)
A reflection reverses orientation, so a clockwise labelling becomes counterclockwise. Lengths, angles and parallelism are preserved.
Answer: 47 (also accepted: 47°)
Translations preserve angle measures, so the image angle is 47°.
Answer: C) They are parallel
Rigid transformations take parallel lines to parallel lines.
Answer: 5
Reflecting over the x-axis changes the sign of the y-coordinate, so (3, -5) maps to (3, 5).
Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments.
A full lesson with slides, activities and an exit ticket on properties of rigid transformations, pitched to grade 8 and editable in PowerPoint or Google Slides.
Make a lesson →A printable, differentiated worksheet on 8.G.A.1 with an answer key, ready in about a minute.
Make a worksheet →Turn properties of rigid transformations into a quiz students answer online that marks itself, with a class summary for you.
Build a test →Translations, reflections and rotations, and any sequence of them. They move a figure without changing its size or shape.
Students are expected to discover and confirm the properties by measuring and comparing, not to prove them formally. Formal proofs come in high school geometry.