GRE Geometry Concepts, Formulas and Questions

GRE Geometry Formulas and Concepts 

The GRE Geometry concepts have certain formulas and rules that need to be followed. GRE Geometry Math problems need to be solved following the formulas and rules for each figure. Candidates need to follow these formulas to achieve a Good GRE Score. The properties, formulas and rules of each concept have been given below.

GRE Geometry Lines 

A line can be defined as a set of infinite points. There are different types of lines which are as follows:

• A straight line that has no end point and extends in both directions.
• A curve line can seem to extend from one point to another changing direction constantly.
• A line segment can be defined as two points having definite end points.

There are certain concepts that need to be considered in GRE Geometry problems for lines and angles.

Concept

There are certain concepts in lines and angles which need to be considered as follows:

• A straight line is equal to 180 degrees
• Two lines that never intersect but has the same slope are parallel lines
• Corresponding angles are equal in measure.
• Alternate interior angles are equal in measure.
• Alternate exterior angles are equal in measure.
• Consecutive interior angles add up to 180 degrees.
• An acute angle is an angle less than 90 degrees.
• An obtuse angle refers to an angle between 90 and 180 degrees.

• A right angle implies 90 degrees and is usually signified by a small square:

• The symbol ∠ is often used to denote an angle. For example: angle A=∠A.
• Two lines that intersect at 90-degree angles are perpendicular to each other:

• When two lines intersect, four angles are created:
• Opposite angles are equal in measure (∠A=∠B, ∠C=∠D).
• Adjacent angles add up to 180 degrees (∠A+∠D=180, ∠A+∠C=180, ∠B+∠D=180, ∠B+∠C=180).

• When two parallel lines intersect eight angles are created
• Corresponding angles are equal in measure.
• Alternate interior angles are equal in measure.
• Alternate exterior angles are equal in measure.
• Consecutive interior angles add up to 180 degrees

GRE Geometry Triangles

GRE Geometry includes concepts of triangles. GRE triangle questions are based on different types of triangles including isosceles, equilateral, right, obtuse, acute and scalene. GRE Geometry problems need to be solved based on a set of concepts and formulas.

Concepts

The concepts of GRE special triangles can be explained as follows:

• Equilateral triangle: all sides of the triangle are equal and each angle is of 60 degrees each
• Isosceles triangle: two sides are equal in length and two opposite angles are equal in measure
• Scalene: all sides are different in length and all angles are different in measure

• Right angle triangle: one of the angles of the triangle is 90° and the longest side is called hypotenuse. The sum of all sides is 180°

Formulas

The formulas in GRE geometry for triangles include the area of the triangle and the Pythagorean Theorem as follows:

Area of Triangle:

A= 1/2 bh

Where b is base and h is height

Pythagorean Theorem:

The theorem states that “sum of the squares of the base and height is equal to the square of the hypotenuse for a right angled triangle”.

In the above image, 

Where c is the hypotenuse, a is the base and b is the perpendicular height.

GRE Geometry Quadrilateral 

GRE Geometry concepts include quadrilaterals of four five types including square, rectangle, rhombus, trapezium and parallelogram. The concepts and formulas are given below for the solving quadrilateral based GRE Geometry problems:

Concepts:

• Square: all the four sides are equal and the angles are at 90°. The diagonals bisect each other at 90°.

Formula:

Area of a square = 

Perimeter of a square= 

• Rectangle: opposite sides of the rectangle are equal and the angles are 90°. The diagonals bisect each other but do not meet at right angles

Formula

Area of rectangle = 

Perimeter of rectangle = 

• Parallelogram: the opposite sides and angles are equal in a parallelogram. The diagonals bisecting each other do not form right angles

Formula

Area of rectangle = 

Perimeter of rectangle = 

• Rhombus: all sides are equal in length and opposite sides are parallel to each other. The diagonals bisecting are perpendicular. Adjacent angles are supplementary implying sum of the angles is 180°

Formulas

Area of Rhombus = 

Perimeter of Rhombus: 

• Trapezium: the base and opposite sides are parallel to each other. The angles, sides and diagonals are not congruent.

Formulas

Area of Trapezium = 

Where L1 is length 1, L2 is length 2 and h is height.

Perimeter: sum of the length of all sides

GRE Geometry Circles 

A circle means a set of points equidistant from a centre on a plane surface. A circle’s perimeter is called the ‘circumference of the circle’. The concepts and formulas would help in solving GRE Circle problems.

Concepts:

• Radius: the line segment joining the centre to any point on the circle.
• Chord: the line segment joining any two points on the circle.
• Diameter: the line segment joining any two points of the circle passing through the centre.

Formulas

Diameter = 

Area = 

Circumference = 2

3D GRE Geometry Concept 

3D geometry in GRE Math Problems mainly deals with cube, cuboid, cylinders, cones and hemisphere. The area and volume of the figures have been given below.

• Cuboid: the volume covered by 6 rectangles is a cuboid

Formulas:

Total surface area = 

Lateral surface area = 2height (length + width)

Volume = 

Length of the longest diagonal = 

• Cube: the volume of a cube is covered by all 6 sides as squares

Formulas:

Volume = 

Lateral surface area = 

Total surface area =

Length of diagonal of cube = 

• Cylinder: a 3 dimensional solid figure with 2 circular and parallel faces connected by a curved surface.
• Major dimensions are radius of base and height

Formulas

Volume = 

Lateral Surface Area = 2

• Cone: 3 dimensional shape which has a circular base and narrows to one point

• The height, radius and slant height are the key measurements

Formulas:

Slant height = 

Volume of a cone = 

Total surface area = 

GRE Coordinate Geometry

The calculations in coordinate geometry are done in coordinate plane axes for GRE Geometry questions. The key component in Coordinate Geometry in the coordinate axis is the number line.

Concepts

A point on the coordinate plane is represented with an ordered pair (x, y) where x is the abscissa and y is the ordinate. The coordinate plane is divided into four quadrants. Candidates need to consider following the GRE Geometry practice problems for preparing for the exam. The formulas to solve this part of GRE Geometry problems are as follows.

Formulas

Distance, 

Theorem: 

Tips for GRE Geometry 

Candidates need to follow the GRE Preparation tips in order to practice for their GRE exam. The following tips can be considered helpful for the candidates.

• Candidates need to memorise the key concepts and formulas in order to solve the GRE Geometry problems
• Candidates need to make flashcards as part of their preparation for the test
• Candidates need to follow effective GRE Geometry Practice Questions to be aware of the types of questions that they might encounter