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GeometryBoost!

We've designed GeometryBoost! as an intro to high school geometry, with a strong emphasis on the logical and definitional foundations that all geometry is based on. We start with logic exercises, including inductive reasoning, conditional statements and their converses; definitions (e.g., lines, points, planes, segments, angles); properties (e.g., identity property, transitive property, reflexive property); and geometry notation. We will tie these concepts to ideas in life (e.g., examples, counterexamples) as well a mathematical concepts that the students know from algebra (e.g., lines on a coordinate plane). From there, we will start working on angles (congruency, angle measures, angles in a triangle, angles in parallel lines cut by a transversal, angles in a circle, etc.), and we start both applying algebra to geometry and writing proper geometric proofs. From angles, we move on to an emphasis on triangles (triangle congruence and congruencies one can derive from congruent triangles. This material largely covers the first semester of a typical geometry class. Throughout the course we'll add in other critical concepts (such as area and perimeter of 2-dimension and 3-dimensional shapes and irregular shapes) and push the students to think about ways to solve related SAT problems (which, while not requiring proofs, require similar thinking).