Illustrative Math Lesson

Alternate Interior Angles: Discovering the Pattern

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8th GradeBTC Style / Thinking Classrooms40 min

Learning Objective

Students will be able to identify alternate interior angle pairs formed by a transversal cutting parallel lines and use their equality to find unknown angle measures.

Lesson Overview

Students discover the Alternate Interior Angles theorem through a thin-sliced progression, moving from identifying angle pairs to using the relationship to solve for unknown angle measures in increasingly complex figures.

Materials

Vertical whiteboards or chart paper
Dry-erase markers (multiple colors if available)
Pencils and scratch paper

Scaffolded Task Progression

1Task 1

The figure below shows two parallel lines

m

and

n

cut by a transversal

t

. The eight angles are numbered 1–8.

[ Interactive graph / diagram, available in the full lesson ]

Part A: Which angles are in the interior region (between the two parallel lines)?

Part B: From those interior angles, which pairs are on *opposite* sides of the transversal? List both pairs.

2Task 2

In the figure below, lines

m ∥ n

are cut by transversal

t

, and

m ∠1 = 65°

.

[ Interactive graph / diagram, available in the full lesson ]

Find

m ∠3

m ∠5

, and

m ∠7

. Show your reasoning for each.

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