Aside from these skills and concepts, students will develop their ability to construct formal logical arguments and proofs in geometric settings and problems. Students demonstrate understanding by identifying and giving examples of undefined terms, axioms, theorems, and inductive and deductive reasoning. Students write geometric proofs, including proofs by contradiction. Students construct and judge the validity of a logical argument. This includes giving counter examples to disprove a statement.
Students prove basic theorems involving congruence and similarity.
Students prove triangles are congruent or similar and are able to use the concept of corresponding parts of congruent triangles. Students know and are able to use the Triangle Inequality Theorem. Students prove and use theorems involving the properties of parallel lines cut by a transversal, the properties of quadrilaterals, and the properties of circles. Students know, derive, and solve problems involving perimeter, circumference, area, volume, lateral area, and surface area of common geometric figures. Students compute the volume and surface area of prisms, pyramids, cylinders, cones, spheres.