Rigid motions are transformations that preserve lengths and angles. If an object or shape is identical (or congruent) before and after the transformations, these transformations are rigid motions. Rigid motions are also called isometries or congruence transformations.

Rigid motion changes the location of a shape, or the direction it is facing, but does not change the size or shape of it. The three basic rigid motions are translation, reflection, and rotation.

In mathematics, a rigid transformation (also called Euclidean transformation or Euclidean isometry) is a geometric transformation of a Euclidean space that preserves the Euclidean distance between every pair of points. The rigid transformations include rotations, translations, reflections, or their combination.

Rigid motion is otherwise known as a rigid transformation and occurs when a point or object is moved, but the size and shape remain the same. This differs from non-rigid motion, like a dilation, where the size of the object can increase or decrease.

There are four types of rigid motions that we will consider: translation , rotation, reflection, and glide reflection. Translation: In a translation, everything is moved by the same amount and in the same direction. Every translation has a direction and a distance.

Remember that if figures are identical in shape and size, they are congruent. Applying rigid transformations to a figure does not change the shape or size, so the image and object are congruent. If one object can be mapped to another by rigid motions, the objects are congruent.

Answer. Rigid motion means form of motion that maintains distance. So the above mentioned forms – reflection, rotation and translation are part of rigid motion. Dilation is non rigid motion.

10 number

5 Non-injective Digitized Rigid Motions.

Dilations

eight rigid motions

A glide reflection is a composition of transformations.In a glide reflection, a translation is first performed on the figure, then it is reflected over a line. Therefore, the only required information is the translation rule and a line to reflect over. You also need a line to reflect over.

Generally a non-rigid transformation is motion that doesn’t preserve the shape of objects. If you look at a typical transformation matrix, rigid transformations would include translation, rotation, and reflection.

Rigid motions map a line to a line, a ray to a ray, a segment to a segment, and an angle to an angle. Rigid motions preserve lengths of segments. Rigid motions preserve the measures of angles.

4. Rigid transformations preserve location in the plane. 5. Corresponding sides in rigid transformations are the same length.

dilation

Side-Side-Side (SSS) Rule Side-Side-Side is a rule used to prove whether a given set of triangles are congruent. The SSS rule states that: If three sides of one triangle are equal to three sides of another triangle, then the triangles are congruent.

SSS (Side-Side-Side) Another way to prove triangles are similar is by SSS, side-side-side. If the measures of corresponding sides are known, then their proportionality can be calculated. If all three pairs are in proportion, then the triangles are similar.

If all the three sides of one triangle are equivalent to the corresponding three sides of the second triangle, then the two triangles are said to be congruent by SSS rule.

There are five ways to find if two triangles are congruent: SSS, SAS, ASA, AAS and HL.