GEOMETRY THEORY AND APPLICATIONS



GEOMETRY THEORY AND APPLICATIONS

NEW PROVIDENCE HIGH SCHOOL

New Providence, NJ

Geometry Theory and Application is developed in conjunction with the use of technology to help students inductively draw conclusions from numerous examples. Students translate real-world situations into mathematical models, obtain solutions, and then translate solutions back into real-life contexts. During this time, accurate mathematical vocabulary is developed and calculations are performed that further the algebraic skills learned in previous courses.

Students bring many geometric experiences with them to high school. In this course, they begin to use more precise definitions and develop careful proofs. Although there are many types of geometry, this course focuses on Euclidean geometry, studied both with and without coordinates. This course begins with an early definition of congruence and similarity with respect to transformations, then moves on through the triangle congruence criteria and other theorems regarding triangles, quadrilaterals and other geometric figures. Students then move on to right triangle trigonometry and the Pythagorean theorem, which extends to the Laws of Sines and Cosines. An important aspect of the Geometry course is the connection of algebra and geometry when students begin to investigate analytic geometry in the coordinate plane. In addition, students work with probability concepts, extending and formalizing their initial work in middle school. They compute probabilities, drawing on area models. Area models for probability can serve to connect this material to the other aims of the course.

To summarize, high school Geometry corresponds closely to the Geometry conceptual category in the high school standards. Thus, the course involves working with congruence (G-CO), similarity (G-SRT), right triangle trigonometry (in G-SRG), geometry of circles (G-C), analytic geometry in the coordinate plane (G-GPE), and geometric measurement (G-GMD) and modeling (G-MG). The Standards for Mathematical Practice apply throughout the Geometry course and, when connected meaningfully with the content standards, allow for students to experience mathematics as a coherent, useful and logical subject.

Geometry Theory and Applications, is the second course in the honors program. Students meet rigorous demands of conceptual understanding, procedural skill and fluency, application, and accuracy. In addition to the content-based knowledge and skills, this course integrates the skills, knowledge, and expertise of 21st Century Learning as identified by the Partnership for 21st Century Skills. Twenty-first Century Learning, when used in combination with standards-based content, ensures that students are prepared for success in today’s challenging environment. In this course, students will gain valuable life-long skills to meet the challenges of a complex global society utilizing differentiation of instruction and state-of-the-art technology.

PREREQUISITES

Honors Algebra I

PROFICIENCY REQUIREMENTS

Attendance: A student enrolled in this class is expected to be present at least 90% of the days the class is in session.

Achievement: A student must achieve at least a D- average for the following: the four marking periods, the mid-term exam, and the final exam.

OBJECTIVES

Upon completion of the course the student will be able to demonstrate proficiency in the following key areas:

➢ Formal geometric constructions using compass and straight edge

➢ Inductive and deductive reasoning leading to formal proof

➢ Relationships between slopes, parallel lines, and perpendicular lines

➢ Analysis of the criteria required for congruent triangles

➢ Relationships within triangles, such as midsegments

➢ Analysis of the attributes of the types of quadrilaterals

➢ Conditions needed for similarity, especially similar triangles and their relationships

➢ Similarity of right triangles to define the meaning of trigonometric ratios

➢ Using the definition of similarity to describe transformations of figures, including reflections, translations, and rotations

➢ Area, surface area, and volume of polyhedra

➢ Give informal arguments using Cavalieri’s principle for the volume formulas of a sphere and other solid figures

➢ Using trigonometric ratios to derive the area formula for triangles

➢ Prove the Law of Sines and Law of Cosines to solve application problems

➢ Relationships of the angles and segments within a circle

➢ Construct a tangent line from a point outside a given circle to the circle.

➢ Using technology to research, create, and present solutions of geometric situations

➢ Solving real world problems involving geometric shapes and concepts

REVISED: 2012

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