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Lesson Plans and Worksheets for Grade 8

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More Math Lessons for Grade 8

Common Core For Grade 8

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).

Student Outcomes

- Students know the definition of congruence and related notation, i.e., ≅ . Students know that to prove two figures are congruent there must be a sequence of rigid motions that maps one figure onto the other.
- Students know the basic properties of congruence are similar to 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.

Exercise 1

a. Describe the sequence of basic rigid motions that shows S_{1} ≅ S_{2}

b. Describe the sequence of basic rigid motions that shows S_{2} ≅ S_{3}

c. Describe the sequence of basic rigid motions that shows S_{1} ≅ S_{3}

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.

Exercise 2

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'?

Lesson Summary:

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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