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Rigid Motions to Transform Figures

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Aligned To Common Core Standard:

High School Congruence - HSG-CO.B.6

What are Rigid Motions to Transform Geometric Figures? The transformation of geometrical shapes in mathematics is an important concept. Any shape that changes its position or orientation from its actual position and orientation is a transformed geometric figure. So, what are rigid motions in transformation? Rigid motions in geometrical transformation are the ones that do not affect the size, shape, or angles of a shape. There are three types of rigid motion in geometry, and these include translation, reflection, and rotation. The translation is the motion of a shape on the x- and the y-axis. The orientation of the translated figure stays the same, while its horizontal and vertical positions change. The reflection of a geometric shape is similar to how we see our reflections in the mirror. The dimensions, angles, and shape remain the same, but the object becomes inverted. The object is reflected over a reference or mirror line. The rotation is when a shape is turned about a center of rotation. Even in this case, the shape, size, and angles remain the same! This selection of worksheets and lessons teaches you how to perform translations, rotations, reflections, and glide reflections.

Printable Worksheets And Lessons

Homework Sheets

It is all about thrown shapes on themselves.

  • Homework 1 - The shape is a diamond and has 4(n) sides. Since n = 4 is even and l passes through the midpoints of two opposite sides, l is a line of symmetry. So, one answer is a reflection across l.
  • Homework 2 - Rotating a parallelogram by 180° carries the parallelogram onto itself.
  • Homework 3 - Since n = 5 is odd and l passes through the midpoints of two opposite sides, l is a line of symmetry. One answer is a reflection across l.

Practice Worksheets

It's interesting to see what kids come up with when you ask them to describe geometric movements.

  • Practice 1 - Describe the transformation that would carry this trapezoid onto itself.
  • Practice 2 - Which type of transformation would carry this regular pentagon onto itself?
  • Practice 3 - We focus a bit on triangles.

Math Skill Quizzes

Most of the translations are one step, but there are a few two step translations here.

  • Quiz 1 - Which of the transformations would carry this polygon onto itself?
  • Quiz 2 - This is polygon based.
  • Quiz 3 - More work on those pesky polygons.