#### Unit 1 - Congruence, Proof, and Constructions

Contains the following Standard Clusters:

• Experiment with transformations in the plane.
• Understand congruence in terms of rigid motions.
• Prove geometric theorems.
• Make geometric constructions.

## Collection Contents

### Cluster - Experiment with transformations in the plane.

by Allen Wolmer

Build on student experience with rigid motions from earlier grades. Point out the basis of rigid motions in geometric concepts, e.g., translations move points a specified distance along a line parallel to a specified line; rotations move objects along a circular arc with a specified center through a specified angle.
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### Cluster - Understand congruence in terms of rigid motions.

by Allen Wolmer

Rigid motions are at the foundation of the definition of congruence. Students reason from the basic properties of rigid motions (that they preserve distance and angle), which are assumed without proof. Rigid motions and their assumed properties can be used to establish the usual triangle congruence criteria, which can then be used to prove other theorems.
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### Cluster - Prove geometric theorems.

by Allen Wolmer

Encourage multiple ways of writing proofs, such as in narrative paragraphs, using flow diagrams, in two-column format, and using diagrams without words. Students should be encouraged to focus on the validity of the underlying reasoning while exploring a variety of formats for expressing that reasoning. Implementation of G.CO.10 may be extended to include concurrence of perpendicular bisectors and angle bisectors as preparation for G.C.3 in Unit 5.
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### Cluster - Make geometric constructions.

by Allen Wolmer

Build on prior student experience with simple constructions. Emphasize the ability to formalize and explain how these constructions result in the desired objects. Some of these constructions are closely related to previous standards and can be introduced in conjunction with them.
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'C' - Curriki rating

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