Embedded Files
Lesson Video
Lesson Video
Focus Standards
Focus Standards
Learning Focus
Learning Focus
Additional Resources
Additional Resources
A Develop Understanding Task
Explores ways of knowing the triangle interior angle sum theorem is true—one based on experiments with specific triangles, the other based on a transformational argument. Introduces students to proof in the form of informal verbal arguments.
NC.M2.G-CO.10
Examine ways of knowing that the sum of the angles in a triangle is .
How do I know something is true? Are there different ways that I know or accept things to be true?
When I notice a pattern in examples or through experimentation, how do I convince myself that my conjecture is always true?
Regardless of the shape or size of a triangle, is there a characteristic that is the same for all triangles in addition to being a three-sided polygon?
A Develop Understanding Task
Develops understanding about how to move from reasoning with a diagram to reasoning from a logical sequence of statements. Explores the logic behind the construction of diagrams. Practices writing symbolic statements to match verbal descriptions.
Examine features of diagrams to determine the story of how the diagrams were built.
Write a paragraph to prove a conjecture that surfaces when analyzing a diagram.
What can I learn by analyzing the features of a geometric diagram?
What assumptions am I making when I interpret the features of a diagram?
Can I tell the story of a diagram: what feature of the diagram was drawn first, because everything else depends on its existence, and what features were drawn later?
How can I write a concise description justifying something new that I noticed while analyzing a diagram?
A Solidify Understanding Task
Examines strategies for sequencing proofs, including proving the points on a perpendicular bisector are equidistant from the endpoints of the segment it intersects.
Organize and sequence proof statements using a two-column format.
Examine a claim about points on a perpendicular bisector of a line segment.
How do I keep track of all of the statements that need to be recorded in a proof?
How do I attend to the order of statements in a proof, so that ideas that need to be established first come before statements that require prior information?
A Solidify Understanding Task
Solidifies understanding of ways to organize proofs about lines, angles, and triangles using flow diagrams and two-column proof formats.
Select and sequence statements for a proof using flow diagrams.
Define lines and line segments related to triangles: medians, altitudes, angle bisectors, and perpendicular bisectors of the sides.
When a lot of things are true about a diagram, how can we identify and organize the statements that must be used to justify a particular claim?
Besides the line segments that form the sides, what other lines and line segments are useful in describing features of a triangle?
A Solidify Understanding Task
Develops statements about parallelism for rigid motion transformations, which will be accepted as postulates.
Determine when a line will be parallel to its pre-image after a translation, rotation, or reflection.
Build a system of geometry based on definitions, postulates, and theorems.
What kinds of transformations produce lines that are parallel to their pre-images?
How are definitions, theorems, and postulates different? Why do we need all three?
A Solidify Understanding Task
Provides opportunity to generate conjectures from a diagram about vertical angles, exterior angles of a triangle, and parallel lines cut by a transversal.
Make conjectures about vertical angles and exterior angles of a triangle by reasoning with a diagram.
Make conjectures about angles formed when a line intersects two or more parallel lines by reasoning with a diagram.
Tessellations are diagrams created by a sequence of repeated figures produced by translations, rotations, or reflections that completely fill a plane with no gaps or overlaps. What do tessellations reveal about relationships between the angles formed when a line intersects two or more parallel lines?
A Practice Understanding Task
Practices writing formal proofs to prove conjectures about vertical angles, exterior angles of a triangle, and parallel lines cut by a transversal. Examines converses of statements.
Practice translating proof-ideas into written formats.
What do I need to attend to when I write a formal proof?
What format should I use: narrative paragraphs, flow diagrams, two-column format? How does each format support my thinking?
What understandings might I draw upon: rigid transformations, triangle congruence, algebra?
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