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.9

Prove theorems about lines and angles. Theorems include: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent; points on a perpendicular bisector of a line segment are exactly those equidistant from the segment’s endpoints.

• Angles
Students are introduced to all kinds of angles in this lesson plan, including acute, obtuse, right, vertical, adjacent, and corresponding among others.
• 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.
• 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.
• 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.
• 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.
• 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.
• Student Task: Floor Pattern
In this task, students will investigate the geometrical properties of a pattern of floor tiles
• Tangent Lines and the Radius of a Circle
This task presents a foundational result in geometry, presented with deliberately sparse guidance in order to allow a wide variety of approaches.

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 - Lindsey Henderson and see the Mathematics - Secondary website. For general questions about Utah's Core Standards contact the Director - Jennifer Throndsen.

These materials have been produced by and for the teachers of the State of Utah. Copies of these materials may be freely reproduced for teacher and classroom use. When distributing these materials, credit should be given to Utah State Board of Education. These materials may not be published, in whole or part, or in any other format, without the written permission of the Utah State Board of Education, 250 East 500 South, PO Box 144200, Salt Lake City, Utah 84114-4200.