Identifying Similar Triangles
This lesson unit is intended to help you assess how students reason about geometry and, in particular, how well they are able to:
- Use facts about the angle sum and exterior angles of triangles to calculate missing angles.
- Apply angle theorems to parallel lines cut by a transversal.
- Interpret geometrical diagrams using mathematical properties to identify similarity of triangles.
- Before the lesson, students work individually on an assessment task designed to reveal their current understanding and ability to reason using geometrical properties. You then review their responses and create questions for students to consider when improving their work.
- After a whole-class introduction, students work in small groups on a collaborative discussion task, categorizing diagrams of pairs of triangles based on their similarity. Throughout their work, students justify and explain their thinking and reasoning.
- Students review their work by comparing their categorizations with those of their peers.
- In a whole-class discussion, students review their work and discuss what they have learned.
- In a follow-up lesson, students review their initial work on the assessment task and work alone on a task similar to the introductory task.
- Each student will need a mini-whiteboard, pen, and wipe, and copies of the assessment tasks Puzzling Triangles and Puzzling Triangles (revisited).
- Each small group of students will need a copy of Sorting Triangles, a pencil, a marker, a large sheet of poster paper, a pair of scissors and a glue stick.
There are also some Blank Cards for students to create some new cards for others to work on if they finish the collaborative lesson activity.
15 minutes before the lesson, a 80-minute lesson (or split into two shorter lessons), and 15 minutes in a follow-up lesson (or for homework). These timings are not exact.
This lesson involves a range of mathematical practices from the standards, with emphasis on:
- MP1: Make sense of problems and persevere in solving them
- MP2: Reason abstractly and quantitatively
- MP3: Construct viable arguments and critique the reasoning of others
- MP5: Use appropriate tools strategically
- MP6: Attend to precision
- MP7: Look for and make use of structure
Mathematical Content Standards
This lesson asks students to select and apply mathematical content from across the grades, including the content standards:
- 8.G: Understand congruence and similarity using physical models, transparencies, or geometry software.