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G-2D-1-8

Page history last edited by Brenda Butz 6 years, 3 months ago

G.2D.1.8 Construct logical arguments to prove triangle congruence (SSS, SAS, ASA, AAS and HL) and triangle similarity (AA, SSS, SAS).

In a Nutshell

Students will begin to formalize their reasoning when deciding if two triangles are congruent. They will consider the corresponding parts of triangles and determine if these parts are congruent and from there students will make deductions about the congruency of the triangles.

Student Actions	Teacher Actions
Develop a Deep and Flexible Conceptual Understanding: Students will use postulates and theorems relating to triangle congruence and triangle similarity in logical arguments and proofs. Develop Mathematical Reasoning: Students will develop their ability to distinguish between correct and incorrect application of triangle congruence and similarity. Develop the Ability to Communicate Mathematically: Students will write both formal and informal proofs showing congruence in a logical step by step manner.	Teachers will promote reasoning and problem solving by implementing tasks that have multiple correct paths to the answer. Teachers will support productive struggle in learning to prove triangles by scaffolding levels of difficulty through teacher involvement to student independence. Teacher will pose purposeful questions to help students form logical arguments in order to write formal and informal proofs. Teachers will elicit and use evidence of student thinking through classroom discussions and group practice.
Key Understandings	Misconceptions

Students understand how to prove triangles congruent by SSS, SAS, ASA, AAS, and HL both formally and informally.
Students understand how to prove triangles are similar by AA, SSS or SAS both formally and informally.

Students confuse the basic concepts of similarity and congruence.
Students interchange ASA and AAS thinking the two methods are the same.
Students try to use SSA as a method to prove congruence.
Students have trouble understanding the terms “included angle” and “included side”.and “non-included angle” and “non-included side.”

OKMath Framework Introduction

Geometry Grade Introduction