Secondary Mathematics II

Strand: GEOMETRY - Similarity, Right Triangles, and Trigonometry (G.SRT)

Understand similarity in terms of similarity transformations (Standards G.SRT.1–3). Prove theorems involving similarity (Standards G.SRT.4–5). Define trigonometric ratios and solve problems involving right triangles (Standards G.SRT.6–8).

Standard G.SRT.5

Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.

• Bank Shot
This task asks students to use similarity to solve a problem in a context that will be familiar to many, though most students are accustomed to using intuition rather than geometric reasoning to set up the shot.
• 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 Conditions for Congruency
This lesson unit is intended to help educators assess how well students are able to work with concepts of congruency and similarity, including identifying corresponding sides and corresponding angles within and between triangles. They will also identify and understand the significance of a counter-example, and prove and evaluate proofs in a geometric context.
• Extensions, Bisections and Dissections in a Rectangle
This task involves a reasonably direct application of similar triangles, coupled with a moderately challenging procedure of constructing a diagram from a verbal description.
• Finding triangle coordinates
The purpose of this task is to use similar triangles in order to study the coordinates of points which divide a line segment in a given ratio.
• GEOMETRY - Similarity, Right Triangles, and Trigonometry (G.SRT) - 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 - Similarity, Right Triangles, and Trigonometry (G.SRT).
• How far is the horizon?
The purpose of this modeling task is to have students use mathematics to answer a question in a real-world context using mathematical tools that should be very familiar to them. The task gets at particular aspects of the modeling process, namely, it requires them to make reasonable assumptions and find information that is not provided in the task statement.
• 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.
• Joining two midpoints of sides of a triangle
This task is closely related to very important material about similarity and ratios in geometry.
• 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.
• 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.
• Pythagorean Theorem
The purpose of this task is to prove the Pythagorean theorem using similar triangles.
• Slope Criterion for Perpendicular Lines
The goal of this task is to use similar triangles to establish the slope criterion for perpendicular lines.
• 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.
• Squaring the Triangle
Students can manipulate the sides of a triangle in this applet in order to better understand the Pythagorean Theorem.
• Tangent Line to Two Circles
The purpose of this task is to use similar triangles, setting up a proportion in order to calculate a side length.
• Tessellations: Geometry and Symmetry
Students can explore polygons, symmetry, and the geometric properties of tessellations in this lesson.
• Unit Squares and Triangles
This problem provides an opportunity for a rich application of coordinate geometry.

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.