About This Chapter
Solving Angle Problems with Triangles & Quadrilaterals - Chapter Summary
In this helpful chapter, you'll study how to solve angle problems with triangles and quadrilaterals. These lessons cover the Pythagorean theorem and its application, as well as some practice problems to help you solidify your understanding. Additional topics include solving 3D problems using the theorem, plus different types of triangles and their properties. After completing this chapter, you should be able to:
- Outline special triangle rules and formulas
- Detail the properties of shapes like trapezoids, polygons, parallelograms and quadrilaterals
- Explain what the hierarchy of quadrilaterals is designed for
- Define line of symmetry as it's used in geometric shapes
- Measure polygon angles and find the sum
- Understand how to find the number of diagonals in a polygon
- Discuss the format of geometric proofs
It's easy to study for an exam or get caught up in class with our professionally designed learning materials. Each lesson is accompanied by a multiple-choice quiz that will help you review these topics and identify any that need more study. Our video lessons are generally less than 10 minutes long and easy to navigate using the video tabs feature found in the Timeline. Feel free to study on your mobile phone, tablet or computer any time that works well for you.
1. Pythagorean Theorem: Definition & Example
Learn what the Pythagorean Theorem says about a right triangle and the relationships of its three sides to each other by watching this video lesson. Also learn how you can use this to your advantage when solving problems.
2. 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.
3. Using the Pythagorean Theorem to Solve 3D Problems
The Pythagorean Theorem is a fascinating formula often used to solve two-dimensional problems. This lesson will explain how to extend this concept to three-dimensional problems in two ways.
4. Types of Triangles & Their Properties
This lesson introduces different types of triangles. We'll discuss some different characteristics that are common to all triangles and some properties that are unique to certain types of triangles.
5. Special Triangle: Rules & Formulas
Finding the missing side of a triangle is pretty simple when that triangle is 'special'. In this lesson, you will learn about two types of special right triangles, their properties and shortcuts to find the missing side length.
6. 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.
7. What is the Hierarchy of Quadrilaterals?
Quadrilaterals are all around us in the real world. This lesson will explore different types of quadrilaterals and look at how to classify various quadrilaterals using definitions that lead to the hierarchy of quadrilaterals.
8. What is a Line of Symmetry in Geometric Shapes?
After viewing this lesson, you should be able to identify shapes that have a line of symmetry in them and know how to find where this line is. A short quiz to test your knowledge will follow the lesson.
9. How to Measure the Angles of a Polygon & Find the Sum
Watch this video lesson to learn the one formula that lets you find the measure of angles in any regular polygon. Also, learn how you can tell if you are working with a regular polygon or not.
10. How to Find the Number of Diagonals in a Polygon
At first, you might think that the diagonals of a polygon are pretty useless, but watch this video lesson to learn how diagonals are used in real life. You will learn the formula to find how many diagonals a polygon has as well as how to use it.
11. Geometric Proofs: Definition and Format
Do you have something to prove? Can you explain why? In this lesson, we'll learn all about geometric proofs, including the parts that comprise a proof.
Earning College Credit
Did you know… We have over 200 college courses that prepare you to earn credit by exam that is accepted by over 1,500 colleges and universities. You can test out of the first two years of college and save thousands off your degree. Anyone can earn credit-by-exam regardless of age or education level.
To learn more, visit our Earning Credit Page
Transferring credit to the school of your choice
Not sure what college you want to attend yet? Study.com has thousands of articles about every imaginable degree, area of study and career path that can help you find the school that's right for you.
Other chapters within the GACE Special Education Mathematics & Science (088): Practice & Study Guide course
- Working with Real Numbers
- Fractions, Decimals, Percents & Ratios
- Understanding Number Theory & Estimation
- Overview of Basic Algebra
- Patterns & Sequences in Algebra
- Characteristics & Relationships of Functions
- Solving Basic Geometric Problems
- Points, Lines, Rays & Angles
- Geometric Relationships in the Coordinate Plane
- Solving Problems Involving Systems of Measurement
- Displaying & Interpreting Data
- Measures of Central Tendency
- Statistical Models & Processes
- Understanding Probability, Combinations & Permutations
- Scientific Inquiry & Design
- Nature of Scientific Knowledge
- Major Developments & Historical Figures in Science
- Collecting & Evaluating Scientific Data
- Science Laboratory & Field Equipment Safety
- Environmental Effects of Science & Technology
- Energy Production & Natural Resource Management
- Science & Technology in Consumer Products
- Atoms, Energy & Matter
- Concepts & Relationships Between Energy & Matter
- Basics of the Periodic Table
- Chemical Compounds & Reactions
- Acid-Base Chemistry
- Solutions & Solubility
- Concepts of Mechanics Overview
- Electricity & Magnetism Overview
- Waves & Optics Overview
- Structure & Function of Cells & Organelles
- Basic Biochemistry of Life
- Basic Genetics
- Evolution, Natural Selection & Biological Diversity
- Hierarchical Classification of Living Things
- Understanding Plant Structures & Function
- Animal & Human Anatomy & Physiology
- Population Dynamics & Ecology
- Rocks, Minerals & Soil Overview
- Earth's Structure, Shape & Processes
- Historical Geology
- Understanding the Earth's Oceans
- Freshwater Characteristics & Processes
- Atmosphere & Weather
- Climate, Seasons & Geography
- Exploring Features of the Solar System
- Earth-Moon-Sun System
- GACE Special Education Mathematics & Science Flashcards