Students have studied the concept of congruent polygons informally since elementary school. In this unit, students formalize their understanding of polygon congruence. Polygons are congruent if and only if all their corresponding sides and angles are congruent. The concept of congruent triangles is explored by examining which parts of a triangle are necessary and sufficient to construct a unique triangle. Students prove congruence of triangles through flowchart, two-column, and paragraph proofs. Corresponding parts of congruent triangles (CPCTC) is used to prove congruence of sides and/or angles. Triangle congruence is used to prove the properties of special quadrilaterals, and those properties are used to make alternative definitions of the special quadrilaterals. Compass and straightedge constructions are reviewed and congruent triangles are applied to justify the transformation. The preservation of the properties of polygons under the rigid transformations is explored. Finally, honors students examine the Königsberg Bridge Problem as it relates to networks and Euler paths.
Instructional Flow (PDF)
Description of the typical order of textbook sections and topics taught in the unit.
Unit 4 Standards for Geometry(PDF)
Explanation of what your child should understand by the end of each unit (enduring understandings), how he/she will get to that understanding (essential questions), and how he/she will be evaluated (indicators).
Content map for Geometry Unit 4 (PDF)
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