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2022 G-2D-1-2

Page history last edited by Brigit Minden 10 months, 4 weeks ago

G.2D.1.2


G.2D.1.2 Use the angle relationships formed by lines cut by a transversal to determine if the lines are parallel and verify, using algebraic and deductive proofs.
 


In a Nutshell

Students will determine if properties of angle relationships formed by the intersection of 2 or more lines and a transversal are appropriate to prove a set of lines are parallel. Students will also verify reasoning through the use of algebraic and deductive proofs.

 

Student Actions

Teacher Actions

  • Develop a Deep and Flexible Conceptual Understanding by determining if two lines are parallel or perpendicular based upon relationships with properties of certain angle pairs (i.e. corresponding angles, supplementary angles, etc.).

  • Develop the Ability to Communicate Mathematically by using properties of angles, parallel lines, and transversals to communicate mathematically with both written and verbal explanations, including the use of formal proofs, regarding why two lines are parallel. 

  • Implement tasks featuring various models intersecting lines that allow students to compare and develop reasoning and problem-solving strategies for proving lines parallel.

  • Build procedural fluency from conceptual understanding by using and applying algebraic concepts and geometric theorems to construct proofs of lines being parallel. 

Key Understandings

Misconceptions 

  • Certain angle relationships must be true to prove 2 or more lines intersected by a transversal are parallel to each other.

    • Alternate interior angle pairs are congruent

    • Alternate exterior angle pairs are congruent

    • Corresponding angle pairs are congruent

    • Consecutive interior angle pairs are supplementary

  • The converse of the Corresponding Angle Theorem, Alternate Interior Angles Theorem, Alternate Exterior Angle Theorem, and Consecutive Interior Angle Theorem are used to prove 2 or more lines are parallel. 

  • Students will assume that there is only one way to prove and verify that lines are parallel by ignoring the various ways that lines can be proved parallel.

  • Students may assume that any pair of congruent angles, such as vertical angles or linear pairs are sufficient to prove lines are parallel instead of verifying other necessary angle relationships.

  • Students may not recognize the correct reason and/or statement when forming an algebraic or deductive proof to prove lines are parallel. 

  Knowledge Connections

Prior Knowledge

Leads to 

  • Solving problems using angle relationships (middle school).

  • Analyze and interpret mathematical models involving lines that are parallel, perpendicular, horizontal, and vertical. (A1.A.4.2) 

  • Apply the properties of special quadrilaterals (square, rectangle, trapezoid, isosceles trapezoid, rhombus, kite, parallelogram) to solve problems involving angle measures and segment lengths using mathematical models, algebraic reasoning, and proofs. (G.2D.1.5) 

 

OKMath Framework Introduction

Geometry Grade Introduction

 

 

 

 

 

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