Prove exterior angles of triangles 2

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Objective

SWBAT prove facts about the exterior angles of a triangle.

Big Idea

More practice proving a tough-to-prove fact about triangles, using transversals.

Lesson Author

Jeff Li MTP

New York, NY

Grade Level

Eighth grade

Subjects

Math

Geometry

Standards

8.G.A.5

Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. For example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so.

MP2

Reason abstractly and quantitatively.

MP3

Construct viable arguments and critique the reasoning of others.

MP7

Look for and make use of structure.

Warm Up

10 minutes

Each day, students complete a warm-up that usually consists of spiraling the previous day's material, in addition to older material. Warm-up problems also sometimes extend lessons that students have encountered before to more unfamiliar contexts.

For a video narrative about how I structure each lesson, and how the warm-up fits in, click here.

Play of the Day

40 minutes

Huddle

10 minutes

Today is about getting more and more kids fluent in their ability to prove this fact, and so I ask a few kids to come up to the board to present proofs, and to get evaluated by their peers. We use two simple questions to evaluate:

1. Is the logic correct?

2. Is the presentation clear and understandable?

At this point, students are developing the habits of mind needed to be strong proof-writers. They establish certain facts, choose the logical and correct sequencing of each step, and make a strong conclusion based on their reasoning. We talk about these three elements as the three elements that form the basis of a strong proof.