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.
Students compute areas of polygons including rectangles, scalene triangles, equilateral triangles, rhombi, parallelograms, and trapezoids. Students determine how changes in dimensions affect the perimeter, area, and volume of common geometric figures and solids. Students find and use measures of sides, interior and exterior angles of triangles and polygons to classify figures and solve problems. Students prove relationships between angles in polygons using properties of complementary, supplementary, vertical, and exterior angles. Students prove the Pythagorean Theorem.