 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).
• Angles
Students are introduced to all kinds of angles in this lesson plan, including acute, obtuse, right, vertical, adjacent, and corresponding among others.
• Classifying Triangles
The goal of this task is to help students synthesize their knowledge of triangles.
• 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.
• Congruent angles in isosceles triangles
The goal of this task is to establish that base angles in an isosceles triangle are congruent.
• Congruent angles made by parallel lines and a transverse
The goal of this task is to prove congruence of vertical angles made by two intersecting lines and alternate interior angles made by two parallel lines cut by a transverse.
• 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.
• Finding the Area of an Equilateral Triangle
This task examines how to calculate the area of an equilateral triangle using high school geometry.
• 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.
• Midpoints of Triangle Sides
The goal of this task is to use similarity transformations to relate two triangles.
• 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.
• Module 6: Similarity & Right Triangle Trigonometry - Student Edition (Math 2)
The Mathematics Vision Project, Secondary Math Two Module 6, Similarity and Right Triangle Trigonometry, introduces the last of the transformations, dilation. A big idea of Module 6 is that two figures are similar if a sequence of rigid transformation and dilations exists that maps one figure onto the other.
• Module 6: Similarity & Right Triangle Trigonometry - Teacher Edition (Math 2)
The Mathematics Vision Project, Secondary Math Two Module 6, Similarity and Right Triangle Trigonometry, introduces the last of the transformations, dilation. A big idea of Module 6 is that two figures are similar if a sequence of rigid transformation and dilations exists that maps one figure onto the other.
• Parallelograms and Translations
The purpose of this task is to apply the definition of a parallelogram in the context of a geometric construction.
• Points equidistant from two points in the plane
This task gives the important characterization of the perpendicular bisector of a line segment as the set of points equidistant from the endpoints of the segment.
• 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.
• Seven Circles I
This task is intended to help model a concrete situation with geometry.
• 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. http://www.uen.org - in partnership with Utah State Board of Education (USBE) and Utah System of Higher Education (USHE).  Send questions or comments to USBE Specialist - Joleigh Honey and see the Mathematics - Secondary website. For general questions about Utah's Core Standards contact the Director - Jennifer Throndsen .