Examples, solutions, worksheets, videos, and lessons to help Grade 8 students know the definition of congruence and the properties for all three rigid motions (translations, rotations, and reflections).
Congruence - the sequence of basic rigid motions that maps one figure onto another.
A sequence to show congruence can be any combination of translation, rotation and reflection.
In summary, if a figure S is congruent S' then S' is also congruent to S. In symbols S ≅ S'. It does not matter whether S comes first or S' does.
a. Describe the sequence of basic rigid motions that shows S1 ≅ S2
b. Describe the sequence of basic rigid motions that shows S2 ≅ S3
c. Describe the sequence of basic rigid motions that shows S1 ≅ S3
Basic properties of all three basic rigid motions
A basic rigid motion maps a line to a line, a ray to a ray, a segment to a segment, and an angle to an angle.
A basic rigid motion preserves lengths of segments.
A basic rigid motion preserves degrees of angles.
Perform the sequence of a translation followed by a rotation of Figure XYZ, where T is a translation along a vector AB and R is a rotation of d degrees (you choose d) around a center O. Label the transformed figure X’Y’Z'. Will XYZ ≅ X’Y’Z'?
Given that sequences enjoy the same basic properties of basic rigid motions, we can state three basic properties of congruences:
(C1) A congruence maps a line to a line, a ray to a ray, a segment to a segment, and an angle to an angle.
(C2) A congruence preserves lengths of segments.
(C3) A congruence preserves degrees of angles.
The notation used for congruence is ≅.
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