Getting Started 
Misconception/Error The student is unable to describe the relationship between the measures of the angles. 
Examples of Student Work at this Level The student may correctly identify the angle pairs as alternate interior and corresponding but is unable to describe the relationship between their measures.

Questions Eliciting Thinking What do you know about the measures of these angles?
Is it important that the lines are parallel?
What do you know about the measures of any angle pair in the diagram? 
Instructional Implications Review the definitions of straight angle, linear pair of angles, supplementary angles, vertical angles, and transversal. Provide instruction on the angle pairs that are formed when two lines are intersected by a transversal. Provide diagrams of two lines intersected by a transversal (some of which include two parallel lines) and assist the student in identifying examples of vertical angles, linear pairs of angles, corresponding angles, alternate interior angles, and sameside interior angles. Give the student additional opportunities to identify each of these angle pairs in diagrams.
Allow the student to explore the relationships among the measures of angles formed by two lines and a transversal using tracing paper. Provide an example of two nonparallel lines intersected by a transversal and an example of two parallel lines intersected by a transversal. Ask the student to trace angles and compare each angle to the corresponding angle at the other vertex. Guide the student to observe that when the lines are parallel, corresponding angles are congruent. Encourage the student to explore the relationships among other angle pairs in the diagram. Summarize the results by stating, when two parallel lines are intersected by a transversal:
 Corresponding angles are congruent.
 Alternate interior angles are congruent.
 Sameside interior angles are supplementary.
Provide a diagram of two parallel lines intersected by a transversal with one angle measure indicated. Ask the student to identify the measures of all other angles in the diagram.
Consider implementing the CPALMS Lesson Plan Special Angle Pairs Discovery Activity (ID 26664), a lesson which allows the student to explore angle pairs formed by parallel lines which are cut by a transversal, or the CPALMS Lesson Plan An Investigation of Angle Relationships Formed by Parallel Lines Cut by a Transversal Using GeoGebra (ID 39484). 
Making Progress 
Misconception/Error The student is unable to clearly justify the relationship between the measures of the angles. 
Examples of Student Work at this Level The student states that the angles in each angle pair have the same measure (or are congruent). However, the student is unable to provide a justification.

Questions Eliciting Thinking How did you determine the angles are equal?
Do you know the names of any of the special angle pairs in the diagram? 
Instructional Implications Ask the student to explain how he or she determined that the angle measures are congruent. Assist the student in developing an appropriate justification based on the approach the student took. For example, if the student used tracing paper to copy one angle and compare it to the other angle, help the student devise an appropriate explanation describing the rigid motions used to confirm the congruence of the angles.
Provide additional opportunities to justify the relationship between the measures of angles formed by parallel lines and a transversal. Assist the student in transitioning from using tracing paper to developing a logical argument. 
Got It 
Misconception/Error The student provides complete and correct responses to all components of the task. 
Examples of Student Work at this Level The student states that the angles in each angle pair are the same measure (or are congruent) and provides an appropriate justification. For example, the student:
 Traces one of the angles and places it on top of the other angle so that the vertex and both sides of the one angle coincide with the vertex and both sides of the other angle.
 Logically reasons that vertical angles are congruent, and when two parallel lines are intersected by a transversal, the alternate interior angles are congruent. For example, the student states that is congruent to since they are vertical and is congruent to since they are alternate interior (or since it was just established in the previous problem) and concludes that must be congruent to .

Questions Eliciting Thinking You used tracing paper to copy one angle and compare it to the other. What rigid motion might describe what you did?
Do you know the name of this kind of angle pair?
Would the measures of and (or and ) still be equal if lines m and n were not parallel? 
Instructional Implications If the student used a tracing paper demonstration to explain the relationship between the angle measures:
 Ask the student to describe a rigid motion that maps one angle onto the other.
 Review previously established angle relationships such as: (1) vertical angles are congruent, and (2) when two parallel lines are intersected by a transversal, alternate interior angles are congruent. Then ask the student to logically reason about the relationship between the angle measures.
Consider implementing other MFAS tasks to further explore the studentâ€™s understanding of angle relationships in the context of parallel lines and a transversal.
