# Geometry

The Geometry Regents exam in New York State covers a variety of topics related to plane geometry, spatial reasoning, and geometric proofs. Here are some key areas typically covered:

**Geometric Concepts and Terminology:**

- Points, lines, rays, and angles.
- Types of angles (acute, obtuse, right, straight).
- Parallel and perpendicular lines.
- Properties of polygons (triangles, quadrilaterals, pentagons, etc.).
- Circles and their properties (circumference, diameter, radius, central and inscribed angles).

**Congruence and Similarity:**

- Congruent and similar figures.
- Corresponding parts of congruent and similar figures (sides, angles).
- Triangle congruence theorems (SSS, SAS, ASA, AAS) and similarity criteria.

**Transformations:**

- Translations, rotations, reflections, and dilations.
- Properties of transformations (preservation of distance, angle, and orientation).
- Compositions of transformations.

**Coordinate Geometry:**

- Distance and midpoint formulas.
- Slope of a line and equations of lines (point-slope form, slope-intercept form, standard form).
- Properties of parallel and perpendicular lines in the coordinate plane.

**Polygons and Polyhedra:**

- Properties of polygons (interior and exterior angles, sum of angles, diagonals).
- Properties of polyhedra (faces, edges, vertices).

**Measurement and Area:**

- Perimeter and area of polygons and circles.
- Surface area and volume of basic solids (prisms, pyramids, cylinders, cones, spheres).

**Geometric Proofs:**

- Inductive and deductive reasoning.
- Proving geometric theorems and postulates using deductive reasoning and logical arguments.
- Construction and justification of geometric constructions.

**Coordinate Proofs:**

- Proving geometric properties using coordinate geometry techniques.

The Geometry Regents exam aims to assess students' understanding of fundamental geometric concepts, their ability to apply geometric principles to solve problems, and their proficiency in constructing and justifying geometric arguments. It includes multiple-choice questions, constructed-response questions, and proof-based questions to evaluate students' knowledge and skills comprehensively.