About This Chapter
Triangles - Chapter Summary
The lessons in this chapter cover basic trigonometry, which is the study of triangles. You'll learn how to use the properties of points, lines, planes, angles, lengths and distances to solve problems. The Pythagorean Theorem and how to use it is explored, as are the laws of sines and cosines. You'll learn about right angle trigonometry and proportional reasoning and how you can use their principles to solve measurement problems.
Several practice lessons are included in this chapter to give you experience solving problems with triangles. By the time you've finished all the lessons, you should have a solid understanding of concepts including:
- Ratios and similarities in trigonometry
- Sines and cosines of complementary angles
- Definition of the Pythagorean Theorem and its importance
- Application of the Pythagorean Theorem
- Solving right triangles
- Using A = ½ ab sin C to find area
- Laws of Sines and Cosines and how to apply them
These concise, engaging videos cover the basics of working with triangles, with experienced instructors who use real life examples to explain the concepts. Each lesson is accompanied by a written transcript, giving you another option for accessing this material.
Practice lessons allow you to utilize what you've studied, and there are multiple-choice quizzes at the end of each video. The questions are linked back to the lesson, making it easy to find and review key topics without re-watching the entire video.
1. Proportional Relationships in Triangles
The perimeters of the two triangles, corresponding medians, corresponding angle bisectors, and corresponding altitudes are all similar. In this lesson, you'll learn about some of the proportional relationships in similar triangles.
2. Triangle Proportionality Theorem
Watch this video lesson to learn all about the triangle proportionality theorem and how you can use this interesting theorem to help you solve problems. Learn how a parallel line can create sides that are proportional to each other.
3. Sine & Cosine of Complementary Angles
In this lesson, we'll look at the relationship between the sine and cosine of complementary angles. We'll discuss where this relationship comes from and explore examples of how it can be used.
4. 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.
5. Trigonometry and the Pythagorean Theorem
Explore how the Pythagorean Theorem can be used in conjunction with trigonometric functions. In this lesson, take an inverse trigonometric function, and define all three sides of a right triangle.
6. Solving Right Triangles Using Trigonometry & the Pythagorean Theorem
The Pythagorean Theorem is one of the most well-known and useful math equations. Its simple form and abundant uses make it one of the most helpful processes to learn in math. In this lesson, learn how to solve right triangles using the Pythagorean Theorem.
7. Using Sine to Find the Area of a Triangle
Since you first started working with triangles in math class, chances are you've been exposed to the formula for the area of a triangle. However, that is only good if you know the height of the triangle. This lesson shows you how to get around that.
8. Law of Sines: Definition and Application
Don't get stuck trying to find missing sides or angles in a triangle. Use the Law of Sines to rescue you from any perilous triangle in which you have just a few pieces of information.
9. Law of Cosines: Definition and Application
In this lesson, we'll learn how to solve problems involving three sides and one angle in a triangle. The Law of Cosines, a modification of the Pythagorean Theorem, will save the day.
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Other chapters within the TExES Mathematics 7-12 (235): Practice & Study Guide course
- About the TExES Math 7-12 Exam
- Real Numbers
- Mathematical Models
- Complex Numbers & the Complex Plane
- Number Theory
- Number Patterns
- Functions and Graphs
- Linear Functions
- Quadratic Functions & Polynomials
- Evaluating Piecewise & Composite Functions
- Rational and Radical Functions
- Inequalities and Absolute Values
- Exponentials & Logs
- The Unit Circle
- Trigonometric Functions
- Using a Scientific Calculator for Calculus
- Understanding Limits in Math
- Understanding Rate of Change
- Calculating Derivatives of Functions
- Derivatives and Graphs
- Optimization in Calculus
- Definite Integrals and Sums
- Integration Applications in Calculus
- Working with Measurement
- Finding Volume, Area & Perimeter
- Introduction to Proofs and Constructions
- Congruence and Similarity
- Real World Shapes
- Coordinate Geometry
- Understanding Transformations in Math
- Conic Sections
- Understanding Vectors
- Measuring & Displaying Data
- Data Distribution Overview
- Sampling in Statistics
- Distribution & Inference in Statistics
- Inference About a Mean
- Regression and Correlation
- Finding Probability
- Probability Distributions and Statistical Inference
- Experiments and Surveys
- Mathematical Process & Perspectives
- Teaching Strategies & Activities for the Math Classroom
- Differentiated Instructional Strategies for the Math Classroom
- Using Student Assessments in the Math Classroom
- TExES Mathematics 7-12 Flashcards