### Geometry

Geometry is a full-year, high school math course for the student who has successfully completed the prerequisite course, Algebra I. The course focuses on the skills and methods of linear, quadratic, coordinate, and plane geometry. In it, students will gain solid experience with geometric calculations and coordinate plane graphing, methods of formal proof, and techniques of construction.

**Introduction:**Student will solve problems using set theory and operations, identify characteristics of postulates and relate geometric theorems on points, lines, and planes**Logic:**Student will use inductive reasoning to draw reasonable conclusions, or deductive reasoning to prove basic theorems, and write conditional statements, converses, inverses and contrapositives.**Angles and Parallels:**Student will identify types of angles, categorize a shape as a polygon or non-polygon, identify different kinds of polygons, and find angle measures of polygons**Congruent Triangles and Quadrilaterals:**Student will identify corresponding parts of congruent triangles, prove congruent parts using different theorems and postulates, and solve for angle measures of congruent polygons.**Similar Polygons:**Student will use facts about similarity to calculate side and angle measures in similar polygons, and use sine, cosine, and tangent values to solve for missing values in triangles.**Circles:**Student will identify different parts of a circle, and angles and arcs created by different lines interacting with circles and calculate their measures.**Area and Volume:**Student will calculate the area, surface area, and volume of varying polygons by breaking them down into smaller and recognizable shapes.**Coordinate Geometry:**Student will graph linear equations and inequalities, use the distance and mid-point formulas to find lengths of segments and perimeters of geometric shapes, and find the equation of a line in various ways.**Transformations:**Student will understand rotations, reflections, dilations and translations in terms of angles, circles, perpendicular lines, and line segments, and find the result of combining multiple transformations.**Geometric Application:**Student will use the functions sine, cosine, and tangent, and the inverse trigonometric functions (sin-1, cos-1, and tan-1) to calculate unknown side lengths in right triangles, calculate densities, and use ratios to calculate unit scales.**Probability:**Student will determine the number of combinations, or permutations, in choosing elements from a set, explain the concept of conditional probability as found in everyday situations, and analyze decisions and strategies using probability concepts.

**State:**National

**Grade Level:**9, 10, 11, 12

**Category:**Math

**Course Length:**Year