Unit 1: Congruence, Structure and Proof
Lesson Video
Focus Standards
Learning Focus
Additional Resources
A solidify Understanding Task
Reviews the defining characteristics of the three rigid transformations and the dilation transformation.
NC.M2.F-IF.1
NC.M2.F-IF.2
NC.M2.G-CO.2
NC.M2.G-CO.4
NC.M2.G-CO.5
NC.M2.G-SRT.1
NC.M2.G-SRT.1.a
NC.M2.G-SRT.1.b
NC.M2.G-SRT.1.c
NC.M2.G-SRT.1.d
Identify the defining features of the translation, rotation, reflection, and dilation transformations.
Use function notation to describe transformations.
What are the defining features of each of the following geometric transformations: translation, rotation, reflection, and dilation?
Why can transformations be treated as functions?
A Solidify Understanding Task
Examines the proof process of experimentation, making conjectures and justifying claims about triangle congruence criteria using rigid transformations.
Justify the triangle congruence criteria using reasoning based on rigid transformations.
Is there a “best” sequence of transformations for showing that two figures are congruent to each other?
What is the minimum information needed to prove that triangles are congruent?
A Solidify Understanding Task
Reviews theorems about vertical angles and angles formed when parallel lines are crossed by a transversal in the context of examining and critiquing student-written samples of proofs.
NC.M2.G-CO.9
Examine characteristics of valid proofs.
What make an argument viable (workable, feasible, practical) and valid (a sound argument based on logic or fact)?
Are there different ways that logic reasoning and valid proof can be provided for the same theorem?
Video: Triangle Congruences
A Solidify Understanding Task
Uses diagrams to introduce and elicit proofs of statements about the properties of parallelograms.
Use theorems about the relationships of angles formed by parallel lines and a transversal to prove properties of parallelograms.
Previously, we made several conjectures about properties of special types of parallelograms: rhombuses, rectangles, and squares. How might we prove that our conjectures about parallelograms are true?
How can we prove a quadrilateral is a parallelogram if we don’t know the opposite sides are parallel? That is, what other characteristics might define a parallelogram?
Video: Proof Writing Help
Video: Overview of Quadrilaterals
A Practice Understanding Task
Builds fluency in identifying parallelograms from information about their specific features. Provides practice of explaining the underlying reasoning used to draw specific conclusions from descriptions.
Classify and justify types of parallelograms based on characteristics of their angles and diagonals.
Can I classify parallelograms as squares, rectangles, or rhombuses based on a few given characteristics or properties, such as characteristics about consecutive angles or characteristics about their diagonals?
A Practice Understanding Task
Practices all of the proof techniques discussed in the unit to prove three theorems about the centers of triangles.
Examine properties of the medians, angle bisectors, and perpendicular bisectors of the sides of triangles.
Construct the center of a circle that will pass through all three vertices of a triangle and the center of a circle that can be drawn in a circle so that it touches all three sides.
Construct the “balancing point” of a triangle.
Given any triangle, can a circle be drawn that passes through all three vertex points of the triangle? Can a circle be drawn that is tangent to all three sides of the triangle? If so, how do we find the center of such circles?