Geometry
Objective.
This course reviews the main concepts in Algebra and applies them to explore foundational Geometric concepts. We begin with points and lines, measurement and transformations, and work our way towards triangles and congruence. In semester 1, we lay the foundation for logical reasoning by examining various approaches to problem solving and writing proofs. Students practice showing the steps in their work and justifying their results using mathematical and logical arguments. The basic symbols and representations of points, lines, segments and angles; the relationships between angles and parallel lines; as well as triangles and their congruence will become paramount during semester 2. We also work on constructions using a compass and a straight edge as well as dynamic geometry software.
In semester 2, the foundations of transformations are extended to similar shapes. We review ratios and apply them to right triangles and trigonometry. We also study circles as well as a variety of other polygons. We also review Probability from a Geometric point of view and study related Statistical concepts. At the end, we return to familiar topics such as area and then leave the flat universe to explore solids in 3 dimensions, their surface area and volume given there is time.
Guiding Principles.
In order to be successful in this class, you should keep these three principles in mind at all times: concentration, cooperation, and consistency.
• Mathematics requires deep concentration and attention to detail. Reduce distractions.
• To successeed at any task, you need cooperation with others. Work together with me and classmates.
• Be consistent in your effort. Daily practice is absolutely necessary. Correcting errors is part of learning.
Effective Study and Learning.
• Come to class on time - be ready and attentive
• Take notes on main ideas - don’t copy details of solutions
• Make questions, write them down, then ask when appropriate
• Review and rewrite notes - discuss with others
• Solve for understanding - practice beyond the required assignments
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