Student Actions

Teacher Actions

• Develop strategies for problem-solving by identifying appropriate strategies to demonstrate the integration of angle relationships formed by the intersections of parallel lines and transversals through the use of various modeling representations.

• Develop mathematical reasoning by using their knowledge of parallel lines, transversals, and angle relationships to evaluate the reasonableness of angle measures.

• Develop the Ability to Make Conjectures, Model, and Generalize by examining and developing conclusions about properties of angle relationships formed by parallel lines and transversals 

• Implement tasks that allow students to explore multiple entry points to promote reasoning and problem-solving by allowing students to discover angle relationships in various models involving the intersection of parallel lines and transversals.

• Use and connect multiple representations of lines and transversals, including perpendicular lines that will require student interpretation of the resulting angle relationships.

• Pose purposeful questions to help students make connections between different angle pair relationships resulting from intersections of parallel lines and transversals.

• Build procedural fluency from conceptual understanding while applying algebra concepts to mathematical situations involving properties of angles from parallel lines and transversals. 

Key Understandings

Misconceptions 

• A transversal can be represented by either a perpendicular line or non-vertical line and will intersect two or more lines. 

• Alternate interior angles are congruent.

• Alternate exterior angles are congruent.

• Same-side (Consecutive) interior angles are supplementary.

• Corresponding angles are congruent.

• Vertical angles are congruent.

• Specific properties for pairs of angle relationships are only true when a transversal intersects two or more parallel lines. 

• Students may believe that all angle pairs are congruent i.e. same side interior angles are actually supplementary.

• Students may not understand that lines must be parallel before specific angle pair properties can be assumed true.

• ​​Students may confuse the angle pair relationships and incorrectly identify specific angle pairs (e.g., state an angle pair represents alternate interior instead of corresponding). 

  Knowledge Connections

Prior Knowledge

Leads to 

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

• Students will have prior knowledge of vertical, complementary, and supplementary angles from middle school. 

• 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)