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Hempfield School District Curriculum: Unit Template Course Title: Geometry - 3273 Unit Title: Congruent Triangles Names of Teachers who Developed Unit: Hundley and Cunfer and Gwyn Dates Developed: July-August 2010 Approximate Dates when Taught During School Year: August –September Approximate Number of Periods: 10 Summary: Students will use their knowledge of corresponding parts of congruent parts of congruent polygons to study and apply postulates and theorems related to triangle congruence. Throughout this chapter, students complete progressively more complex proofs. Print Materials Needed: Prentice Hall Mathematics Textbook, note-sheets for each section. Resources: Internet Resource Links: Geometer’s Sketchpad Essential Questions (Include PA Standards, Anchors & Eligible Content) Big Ideas: Numbers, measures, expressions, equations, and inequalities can represent mathematical situations and structures in many equivalent forms. Some geometric relationships can be described and explored as functional relationships There are some mathematical relationships that are always true and these relationships are used as the rules of arithmetic and algebra and are useful for writing equivalent forms of expressions and solving equations and inequalities. Mathematical statements can be justified through deductive and inductive reasoning and proof. Congruence describes a special similarity relationship between objects and is a form of equivalence. Relations and functions are mathematical relationships that can be represented and analyzed using words and equations. Objects can be transformed in a number of ways. Transformations can be described and analyzed mathematically. Essential Questions: What conditions must be true in order to prove two triangles congruent? How do you identify corresponding parts of congruent triangles? What are the properties of an isosceles triangle? Equilateral? How can you tell whether a triangle is isosceles or equilateral? How can you identify and apply special segments in triangles? How do you determine if three segment lengths can form a triangle? 1 Hempfield School District Curriculum: Unit Template What are the relationships between the interior and exterior angles of a triangle? How do you use coordinate Geometry to find relationships within triangles? Assessment Anchors: Eligible Content: Know Vocabulary: Congruent Polygons Side-Side –Side Postulate Side-Angle-Side Postulate Angle-Side-Angle Postulate Angle-Angle-Side Postulate Corresponding Parts of Congruent Triangles are Congruent(CPCTC) Isosceles Triangle – legs, base, vertex angle, base angles, corollary, Hypotenuse leg theorem Understand Do Students will understand: The students will be able to: Name congruent parts Find congruent triangles Proving triangles congruent Use SSS, SAS, ASA, AAS, HL to prove triangles congruent. Use the Isosceles triangle theorems Do proofs using HL theorem Do proofs using CPCTC Stage 2: Assessment Evidence Assessments/Performance Tasks Rubric Titles Benchmark(s) for Course: Unit’s key Assessments Self-Assessments Other Evidence, Summarized Stage 3: Learning Activities 2 Hempfield School District Curriculum: Unit Template Differentiation: Readiness . Profile: Learning Styles / Multiple Intelligences Interest Accommodations for ELLs: 3