Secondary Mathematics II

Strand: GEOMETRY - Congruence (G.CO)

Prove geometric theorems. Encourage multiple ways of writing proofs, such as narrative paragraphs, flow diagrams, two-column format, and diagrams without words. Focus on the validity of the underlying reasoning while exploring a variety of formats for expressing that reasoning (Standards G.CO.9–11).

Standard G.CO.11

Prove theorems about parallelograms. Theorems include: opposite sides are congruent, opposite angles are congruent, the diagonals of a parallelogram bisect each other, and conversely, rectangles are parallelograms with congruent diagonals.

• Congruence of parallelograms
Triangle congruence criteria have been part of the geometry curriculum for centuries. For quadrilaterals, on the other hand, these nice tests seem to be lacking. This task addresses this issue for a specific class of quadrilaterals, namely parallelograms.
• Evaluating Statements About Length and Area
This lesson unit is intended to help educators assess how well students can understand the concepts of length and area, use the concept of area in proving why two areas are or are not equal, and construct their own examples and counterexamples to help justify or refute conjectures.
• GEOMETRY - Congruence (G.CO) - Sec Math II Core Guide
The Utah State Board of Education (USBE) and educators around the state of Utah developed these guides for the Secondary Mathematics II - Congruence (G.CO).
• Introduction to the Materials (Math 2)
Introduction to the Materials in the Mathematics Two of the The MVP classroom experience begins by confronting students with an engaging task and then invites them to grapple with solving it. As students ideas emerge, take form, and are shared, the teacher orchestrates the student discussions and explorations towards a focused mathematical goal. As conjectures are made and explored, they evolve into mathematical concepts that the community of learners begins to embrace as effective strategies for analyzing and solving problems.
• Is this a parallelogram?
This task develops an alternative characterization of a parallelogram in terms of congruence of opposite sides.
• Midpoints of the Sides of a Paralellogram
This is a reasonably direct task aimed at having students use previously-derived results to learn new facts about parallelograms, as opposed to deriving them from first principles.
• Module 5: Geometric Figures - Student Edition (Math 2)
The Mathematics Vision Project, Secondary Math Two Module 5, Geometric Figures. Formal proof is introduced in this module, beginning with students understanding the ways of knowing continuum based on authority, on experience with a few examples, on reasoning from a diagram and on statements accepted as true by the community of practice, including postulates, definitions and theorems.
• Module 5: Geometric Figures - Teacher Edition (Math 2)
The Mathematics Vision Project, Secondary Math Two Module 5, Geometric Figures. Formal proof is introduced in this module, beginning with students understanding the ways of knowing continuum based on authority, on experience with a few examples, on reasoning from a diagram and on statements accepted as true by the community of practice, including postulates, definitions and theorems.
• Parallelograms and Translations
The purpose of this task is to apply the definition of a parallelogram in the context of a geometric construction.
• Proofs of the Pythagorean Theorem
This lesson unit is intended to help educators assess how well students are able to produce and evaluate geometrical proofs.
• Solving Geometry Problems: Floodlights
This lesson unit is intended to help educators assess how well students are able to identify and use geometrical knowledge to solve a problem.
• Student Task: Circles in Triangles
In this task, the students have to find the radius of circles inscribed in various sizes of right triangle.