# Ch 12: Geometric Properties of Objects: Tutoring Solution

### About This Chapter

## How it works:

- Begin your assignment or other GMAT prep work.
- Identify the geometric properties of objects 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 GMAT prep tutoring solution will benefit any student who is trying to learn geometric properties of objects and prepare for the exam. This resource can help students including those who:

- Struggle with understanding properties of shapes, similar triangles, parallel and perpendicular lines, angles, the Pythagorean Theorem or any other geometric properties of objects topic
- Have limited time for studying
- Want a cost effective way to supplement their learning
- Prefer learning geometry visually
- Find themselves struggling to prepare for the GMAT
- Cope with ADD or ADHD
- Want to get ahead in preparing for the GMAT
- Don't have access to their GMAT prep instructor outside of class

## Why it works:

**Engaging Tutors:**We make learning about geometric properties of objects 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 GMAT tutor, these video lessons are thoroughly reviewed.**Convenient:**Imagine a tutor as portable as your laptop, tablet or smartphone. Learn about geometric properties of objects 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:

- Examine the properties of rectangles, rhombuses and squares.
- Identify the properties of quadrilaterals, trapezoids, polygons and parallelograms.
- Explore the applications of similar triangles.
- Learn about the properties of similar and congruent shapes.
- Discover how to apply scale factors to the volume, area and perimeter of similar figures.
- Create parallel, perpendicular and transverse lines.
- Identify different types of angles.
- Apply the Pythagorean theorem.

### 1. Properties of Shapes: Rectangles, Squares and Rhombuses

What's the difference between a square and a rectangle? What about a rhombus and a square? In this lesson, we'll look at the properties of these shapes.

### 2. Properties of Shapes: Quadrilaterals, Parallelograms, Trapezoids, Polygons

Four-sided objects are more than just squares and rectangles. In this lesson, we'll discuss quadrilaterals, parallelograms and trapezoids. We'll also discuss polygons, objects that can have more sides than you can count.

### 3. How to Identify Similar Triangles

Similar triangles have the same characteristics as similar figures but can be identified much more easily. Learn the shortcuts for identifying similar triangles here and test your ability with a quiz.

### 4. Applications of Similar Triangles

Similar triangles are used to solve problems in everyday situations. Learn how to solve with similar triangles here, and then test your understanding with a quiz.

### 5. Properties of Congruent and Similar Shapes

In this lesson, we'll look at triangles, rectangles and other shapes that share properties. This includes both congruent and similar shapes. We'll also practice identifying the missing properties of these shapes.

### 6. Applying Scale Factors to Perimeter, Area, and Volume of Similar Figures

How do shapes change sizes yet retain their proportions and similarities to other shapes? In this lesson, we'll look at what a scale factor is and how to apply it. We'll consider scale factors with regards to three different aspects of similar shapes: perimeter, area and volume.

### 7. Parallel, Perpendicular and Transverse Lines

What are the different types of lines? Where are they visible in the real world and how can you recognize them? Find out here and test your knowledge with a quiz.

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

In addition to basic right, acute, or obtuse angles, there are many other types of angles or angle relationships. In this lesson, we will learn to identify these angle relationships and discuss their measurements.

### 9. Angles and Triangles: Practice Problems

Want more practice solving with angle pairs? How about more review for solving angles in triangles? Look no further. Get more practice here, and test your ability with a quiz.

### 10. The Pythagorean Theorem: Practice and Application

The Pythagorean theorem is one of the most famous geometric theorems. Written by the Greek mathematician Pythagoras, this theorem makes it possible to find a missing side length of a right triangle. Learn more about the famous theorem here and test your understanding with a quiz.

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### Other Chapters

Other chapters within the GMAT Prep: Tutoring Solution course

- Basic Arithmetic Calculations: Tutoring Solution
- Rational Numbers: Tutoring Solution
- Decimals and Percents: Tutoring Solution
- Data & Statistics: Tutoring Solution
- Basic Algebraic Expressions: Tutoring Solution
- Exponents: Tutoring Solution
- Algebraic Linear Equations & Inequalities: Tutoring Solution
- Algebra - Absolute Value Equations & Inequalities: Tutoring Solution
- Algebra - Polynomials: Tutoring Solution
- Algebra - Rational Expressions: Tutoring Solution
- Perimeter, Area & Volume: Tutoring Solution
- Geometric Graphing Basics: Tutoring Solution
- Geometric Graphing Functions: Tutoring Solution
- Conventions in Writing - Grammar: Tutoring Solution
- Usage Conventions in Writing: Tutoring Solution
- Reading Comprehension for Test-Taking: Tutoring Solution
- Critical Reasoning for Test-Taking: Tutoring Solution
- Practical Applications for Test-Taking: Tutoring Solution
- Essay Writing Basics: Tutoring Solution
- Essay Clarity: Tutoring Solution
- Editing Your Writing: Tutoring Solution
- Practicing Analytical Writing: Tutoring Solution