The first three-quarters of this course will be a rigorous and thorough excursion into plane and solid Euclidean geometry, including an examination of geometry as an axiomatic system and the role of a variety of types of formal mathematical proof.  The first quarter will deal with mathematical logic and rules of inference, angles and triangles, congruency, geometric inequalities of the triangle, and perpendicularity. The second quarter will cover parallelisms, quadrilaterals and their properties, the Pythagorean Theorem, and similarity. The third quarter will be devoted to the study of circles and spheres, arcs and sectors, areas and volumes, and coordinate geometry techniques. Formal and informal proof techniques will be utilized throughout the geometry content.  The geometry portion of the course terminates after three quarters so that the fourth quarter of the summer session can be devoted to topics from Algebra 2, including the basic properties and operations of radicals, an introduction to fractional exponents, completing the square to find the center and radius of a circle, operations with rational expressions, and determining the domain of a rational expression.  Additional topics from analytic geometry will be included if time permits.