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Ch 19: GRE Quantitative Reasoning - Plane Geometry: Tutoring Solution

About This Chapter

The Quantitative Reasoning - Plane Geometry chapter of this GRE Prep Tutoring Solution is a flexible and affordable path to reviewing plane geometry. These simple and fun video lessons are each about five minutes long, and they teach all of the information involving plane geometry required for the GRE.

How it works:

  • Begin your GRE review.
  • Identify the plane geometry concepts that you're stuck on.
  • Find fun videos on the topics you need to understand.
  • Press play, watch and learn!
  • Complete the quizzes to test your understanding.
  • As needed, submit a question to one of our instructors for personalized support.

Who's it for?

This chapter of our GRE prep tutoring solution will benefit any student who is trying to prepare for the GRE and earn acceptable scores. This resource can help students including those who:

  • Struggle with understanding angles, properties of shapes or any other plane geometry topic
  • Have limited time for studying
  • Want a cost effective way to supplement their GRE preparation
  • Prefer learning GRE topics visually
  • Find themselves struggling with their plane geometry review
  • Cope with ADD or ADHD
  • Want to get ahead in preparing for the GRE
  • Need access to GRE prep materials

Why it works:

  • Engaging Tutors: We make preparing for the GRE simple and fun.
  • Cost Efficient: For less than 20% of the cost of a private tutor, you'll have unlimited access 24/7.
  • Consistent High Quality: Unlike a live GRE prep tutor, these video lessons are thoroughly reviewed.
  • Convenient: Imagine a tutor as portable as your laptop, tablet or smartphone. Review plane geometry on the go!
  • Learn at Your Pace: You can pause and rewatch lessons as often as you'd like, until you master the material.

Learning objectives:

  • Identify various types of angles and angle relationships.
  • Learn to calculate the perimeter and area of triangles and rectangles.
  • Find out how you can translate complex problems into simple images.
  • Review how to find the area and circumference of circles.
  • Compare and contrast the properties of squares, rectangles and rhombuses.
  • Learn to solve problems using similar triangles.
  • Review how to apply the Pythagorean theorem.
  • Explore types and properties of special right triangles.
  • Find out how to calculate the volume of basic shapes.

13 Lessons in Chapter 19: GRE Quantitative Reasoning - Plane Geometry: Tutoring Solution
Test your knowledge with a 30-question chapter practice test
Types of Angles: Vertical, Corresponding, Alternate Interior & Others

1. Types of Angles: Vertical, Corresponding, Alternate Interior & Others

Understanding angles and angle relationships allows for easier calculation of angle measurement. Learn how to define various types of angles, including vertical, corresponding, alternate interior angles, and how to calculate degree measurement using angle relationships.

Perimeter of Triangles and Rectangles

2. Perimeter of Triangles and Rectangles

Perimeter is defined as the combined distance around a shape, object, or figure, while the perimeter of any polygon can be determined by adding the length of all sides. Learn about perimeter, how to use mathematical formulas to calculate the perimeter of triangles and rectangles, and how to use perimeter to determine the length of unknown polygon sides.

Area of Triangles and Rectangles

3. Area of Triangles and Rectangles

The area of a two-dimensional shape represents the space covered within its perimeter, but area calculations change depending on the shape. Learn how to calculate and solve the areas of right triangles, oblique triangles, and rectangles.

Angles and Triangles: Practice Problems

4. Angles and Triangles: Practice Problems

When solving angles, they should be equal to each other or added together to equal 180, and with solving triangles, all angles in every triangle added together must equal 180 degrees. Engage in practice problems solving angles and triangles.

How to Solve Visualizing Geometry Problems

5. How to Solve Visualizing Geometry Problems

Visualizing geometry problems involves knowing the expected results, and identifying the important pieces of information to make sure all the mathematical details match the word problem. See several examples of how to solve these problems correctly.

Circles: Area and Circumference

6. Circles: Area and Circumference

Like all geometric shapes, circles take up space and a formula is required to calculate the area. Learn about the area and circumference of circles, explore the formula to calculate a circle's area, and review examples that use the diameter and others that use the circumference to find the area of a circle.

Properties of Shapes: Rectangles, Squares and Rhombuses

7. Properties of Shapes: Rectangles, Squares and Rhombuses

Different objects come in different shapes that help achieve their purpose. Learn about the properties of different shapes, including rectangles, squares, and rhombuses.

Applications of Similar Triangles

8. Applications of Similar Triangles

Similar triangles have the same shape but differ in size. Learn about the applications of similar triangles, including how to use them and how to solve real-world problems with similar triangles.

How to Identify Similar Triangles

9. How to Identify Similar Triangles

Similar triangles are defined as two triangles that possess proportional corresponding sides and congruent corresponding angles. Triangle similarity theorems use angle and side comparisons to determine whether two triangles are similar. Learn about the language of similarity, triangle similarity theorems (Angle-Angle, Side-Angle-Side, & Side-Side-Side), and how to use theorems to identify similar triangles.

The Pythagorean Theorem: Practice and Application

10. The Pythagorean Theorem: Practice and Application

Discover how the Pythagorean theorem helps people to solve for all sides of a triangle. Learn about the basics, purpose, and applications of the Pythagorean theorem.

Special Right Triangles: Types and Properties

11. Special Right Triangles: Types and Properties

There are two types of special right triangles that have either 30-60-90 degree angles or 45-45-90 degree angles. Learn more about the definitions and explore the properties of 30-60-90 and 45-45-90 degree angles of special right triangles through examples.

Finding Distance with the Pythagorean Theorem

12. Finding Distance with the Pythagorean Theorem

The Pythagorean theorem outlines principles for right triangles, but it can also be used to calculate distance between points. Learn how this theorem is applied to practical examples of ice cream, skateboard ramps, and even the cliff-peak in 'The Lion King.'

How to Calculate the Volumes of Basic Shapes

13. How to Calculate the Volumes of Basic Shapes

The basic formula for volume is length * width * height and is necessary in geometry and the science of understanding mass in the form of basic shapes. Learn more about how to calculate the volumes of basic shapes and use the methodologies.

Chapter Practice Exam
Test your knowledge of this chapter with a 30 question practice chapter exam.
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Practice Final Exam
Test your knowledge of the entire course with a 50 question practice final exam.
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More Exams
There are even more practice exams available in GRE Quantitative Reasoning - Plane Geometry: Tutoring Solution.

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