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Content Writer - Study Abroad | Updated On - Jun 20, 2024
GRE Geometry is one of the important sections in GRE Quantitative Reasoning. 15% of the questions in Quantitative Reasoning are focused on GRE Geometry questions. GRE Math Geometry has 20 questions in 2 sections, and candidates need to complete the section in 35 minutes. Geometry GRE questions include high school mathematics and statistics. To solve GRE geometry problems, candidates must have a better understanding of elementary mathematical concepts.
![alt tags](https://images.collegedunia.com/public/image/aaa1_dd127e22a2c5f8f859ad1b17df5cef31.png?tr=w-700,h-414,c-force)
GRE Geometry includes concepts including lines and angles, triangles, quadrilaterals, circles, 3D Geometry, and Coordinate Geometry. Candidates are advised to follow the GRE exam pattern to gather an adequate knowledge of the types and number of questions. Geometry GRE questions include multiple choice, quantitative comparisons, and numeric entry-type questions.
Table of Contents |
Overview of GRE Geometry Concepts
GRE Geometry concepts include lines and angles, triangles, 3D Geometry, Quadrilateral circles and coordinate geometry. All of these include further concepts and properties of their own. The average score in GRE Quant is 152.57 out of 170. The following table provides an overview of the GRE Geometry concepts.
GRE Concepts | Items included in GRE Concepts |
---|---|
Lines and Angles |
|
Triangles |
|
Quadrilateral |
|
Circles |
|
3D Geometry |
|
Coordinate Geometry |
|
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.
![GRE Geometry lines](https://images.collegedunia.com/public/image/3100afadc234f8cb6d079a0ce13ce793.png?tr=w-800,h-254,c-force?tr=w-800,h-254,c-force)
- A right angle implies 90 degrees and is usually signified by a small square:
![Right angle](https://images.collegedunia.com/public/image/627e6f6a0277210a1242936a6af39ee1.png?tr=w-300,h-300,c-force?tr=w-300,h-300,c-force)
- 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:
![Two lines intersect](https://images.collegedunia.com/public/image/8931f6c2804775d639cf38bfe42761de.png?tr=w-288,h-247,c-force?tr=w-288,h-247,c-force)
- 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).
![Intersect 4 angle](https://images.collegedunia.com/public/image/c2bd658eb4c9298dd3f0b826870955a6.png?tr=w-223,h-291,c-force?tr=w-223,h-291,c-force)
- 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
![GRE special traingle](https://images.collegedunia.com/public/image/1ea26985409648a555c877c6029aa2c3.png?tr=w-717,h-307,c-force?tr=w-717,h-307,c-force)
- 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”.
![Pythagorean Theorem](https://images.collegedunia.com/public/image/cea0b24041041c02caa6630b0012df48.png?tr=w-274,h-159,c-force?tr=w-274,h-159,c-force)
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°.
![Sqaure](https://images.collegedunia.com/public/image/e1c4bdb57ae9b410381414a269c1a4ea.png?tr=w-190,h-193,c-force?tr=w-190,h-193,c-force)
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
![Rectangle](https://images.collegedunia.com/public/image/7d1b3df7604b7c5e77dd111dc5054049.png?tr=w-302,h-182,c-force?tr=w-302,h-182,c-force)
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
![Parallelogram](https://images.collegedunia.com/public/image/741a908acf988f4768a05611f5f6ba93.png?tr=w-266,h-165,c-force?tr=w-266,h-165,c-force)
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.
![circles](https://images.collegedunia.com/public/image/d67b5a8cacecd896a0eb4f6ac875b6ff.png?tr=w-220,h-220,c-force?tr=w-220,h-220,c-force)
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
![Cuboid](https://images.collegedunia.com/public/image/7f3018d1865801f82bd4071a3b34176f.png?tr=w-225,h-163,c-force?tr=w-225,h-163,c-force)
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
![cube](https://images.collegedunia.com/public/image/5e0135d0accb9a632bae882378510d9f.png?tr=w-179,h-143,c-force?tr=w-179,h-143,c-force)
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
![cone](https://images.collegedunia.com/public/image/bd2e119e003fcbb6bbb69f4320846482.png?tr=w-135,h-177,c-force?tr=w-135,h-177,c-force)
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:
GRE Geometry Books
GRE books for geometry provides tips and strategies for candidates to enhance their scores. Here are a few GRE books for geometry:
- GRE Prep Book By Magoosh-Check PDF
- Manhattan Prep 5 lb. Book of GRE Practice Problems-Check PDF
-
The Official Guide to the GRE® General Test, Third Edition- Check PDF
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.
- Memorize key concepts.
- Regular practice with realistic sample papers.
- Make flashcards.
- Draw a picture.
- Plug to a formula and solve it.
- Approach inscribed shapes as two separate shapes.
GRE Geometry Practice Papers
GRE geometry includes a various type of questions. Candidates need to regularly solve GRE geometry practice problems for better preparation. Here are some GRE practice papers for geometry problems for better practice:
FAQs
Ques: Is geometry important for GRE?
Ques: How many geometry questions are on the GRE?
Ques: What is the basic geometry for GRE?
Ques: What formulas should you know for the GRE?
Ques: How much geometry is on the GRE?
Ques: Is geometry important for GRE?
Ques: What is the syllabus for geometry in GRE?
Ques: What math is mostly on the GRE?
Ques: Is a 160 quantitative GRE score good?
Ques: What is included in the quantitative portion of the GRE?
Ques. What topics in geometry should I focus on for the GRE?
Ans. Focus on fundamental concepts such as lines, angles, triangles, circles, polygons, and three-dimensional shapes. Also, be prepared for coordinate geometry and basic trigonometry.
Ques. Do I need to memorize all the geometric formulas for the GRE?
Ans. While it's essential to know common formulas, the GRE typically provides necessary formulas in the questions. However, knowing them can save you time and boost your confidence.
Ques. How can I improve my visualization skills for geometry questions?
Ans. Practice drawing diagrams and visualizing geometric shapes. Use graph paper or online geometry tools to help you visualize problems.
Ques. Are there any shortcuts or tricks for solving geometry problems quickly?
Ans. Yes, learn about special geometric properties, such as the Pythagorean theorem, similar triangles, and properties of circles, as they can help you solve problems more efficiently.
Ques. What should I do if I can't solve a geometry problem on the GRE?
Ans. If you're stuck on a problem, make an educated guess and mark it for review. Come back to it later if you have time after completing the easier questions.
Ques. Should I use the calculator for geometry problems?
Ans. The GRE calculator is limited and may not be necessary for most geometry questions. It's better to rely on your math skills and only use the calculator when absolutely needed.
Ques. Are there any specific strategies for tackling geometry questions in the GRE Quantitative section?
Ans. Start by reading the question carefully, draw a diagram if necessary, and use process of elimination for multiple-choice questions. Always check your answers if time permits.
Ques. Are there any common pitfalls to avoid in GRE geometry questions?
Ans. Be cautious with misreading questions, assuming information not given, and making careless errors when performing calculations. Double-check your work.
Ques. Can I use scratch paper for geometry calculations in the GRE exam?
Ans. Yes, you will be provided with scratch paper at the test center. Use it for calculations, drawing diagrams, and working through geometry problems.
Ques. What resources can I use to practice GRE geometry questions?
Ans. There are various GRE prep books, online courses, and practice tests that include geometry questions. Additionally, ETS (Educational Testing Service), the organization that administers the GRE, offers official GRE test prep materials, including practice questions with detailed explanations.
*The article might have information for the previous academic years, which will be updated soon subject to the notification issued by the University/College.
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