**Squares:**

Area | A = S^2 (S = Side) |

Perimeter | P = 4s |

**Rules of Angles:**

- An acute angle is equal to 180 degrees
- A right angle is equal to 90 degrees
- An Obtuse angle is an angle between 90 and 180 degrees
- A straight line is 180 degrees
- Two lines that can never intersect and have the same slope are termed parallel lines
- When two parallel lines are intersected by a third line, it forms eight angles

- Two lines that intersect to form four congruent angles are called perpendicular lines. All of the four angles have a measure of 90 degrees.

**1.Circles:**

Area | A = πr^2 |

Area of Sector | Area of sector = πr^2*
central angle of sector /360 |

Length of an Arc | Arc length = 2πr*central length of arc/360 |

Circumference | C=2*π*r |

**4.Rectangles:**

Area | A = L*w |

Perimeter | P = 2l+ 2w |

**5.Polygons:**A polygon is by definition a closed figure which is formed by three or more line segments called sides. Some examples of polygons are — Pentagon, Triangle and Quadrilateral. If a polygon has n sides, it can be divided into (n-2) triangles. A polygon in which all the sides and all interior angles are congruent is called a regular polygon. The perimeter of a polygon is the sum of the length of its sides, the area of the polygon is the area of the region enclosed by the polygon.

**Triangles**

**Equilatera**l – All sides are equal and all interior angles are 60 degrees**Isosceles**– Two sides are equal and the two angles opposite the two equal sides are equal in measure**Right**– A triangle with just one right angle. The side which is the longest (opposite the right angle) is called the hypotenuse and the two shorter sides are the “legs”.

**Pythagorean Theorem:**

Area | A = ½*b*h ; where b=base, h=height |

**Trapezoids:**

Area | A = ½ (a+b)h ; where a=base 1, b= base 2, h=height |

**Rectangular Solids:**

Surface Area | SA = 2 (lw+lh+wh) |

Volume | V = lwh ; where l=length, w=width, h= height |

**Parallelograms:**

Area | A = bh ; where b=base, h=height |

**Right Circular Cylinders:**

Surface Area | SA = 2πr^2 +2πrh ; where r= radius of circular section, h= height |

Volume | V = πr^2 *h |

**Tips and Tricks to Solve GRE Geometry Questions:**

- Besides concepts of geometry, it is recommended that you first learn the key concepts like — the formula (perimeter, area, volume, circumference), the properties, relationship between angles.
- Another tip is to create flashcards with all important terms including diagrams and shapes of the geometric figures you are learning about.
- You can test your knowledge by practicing GRE geometry practice questions. This will help you to evaluate yourself and determine your familiarity with the concepts. These will also give you an idea of how the questions will be asked in the exam.
- On the day of the exam, don’t make assumptions of any values or terminologies in the given geometry questions.
- Many of the geometry questions in the exam don’t have a reference picture. So it is recommended that you draw a figure to help you understand the question in a better manner.

Good Luck!

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