About This Chapter
PSAT Math: Triangles and Trigonometric Ratios - Chapter Summary
Discover what you need to know about triangles and trigonometric ratios in order to answer corresponding questions on the PSAT Math examination. This chapter contains animated video lessons that can help you understand more about the sides and angles of scalene, isosceles and equilateral triangles. The chapter also explains the particulars of the Side-Side-Side (SSS), Angle-Angle (AA) and Side-Angle-Side (SAS) similarity theorems. The use of the entertaining lessons can help you to:
- Review the properties of triangles, including obtuse and equilateral
- Understand the language of similarity and similar triangle theorems
- Solve problems with similar triangles
- Identify the properties of a special right triangle
- Understand sine and cosine trigonometry problems
- Define a trigonometric ratio and solve practice equations
- Apply the Pythagorean theorem and use it to calculate distance traveled
These online video lessons teach through the use of graphics and conversational narration. Math experts present the lessons, and they answer your interactively submitted questions. Study triangles and trigonometric ratios in your spare moments. Check out the written transcripts that include bold key words. By taking the short, multiple-choice quizzes, you can become more familiar with the kinds of questions you'll encounter on the PSAT Math examination.
PSAT Math: Triangles and Trigonometric Ratios Chapter Objectives
You'll have a chance to demonstrate what you've learned about triangles and trigonometric ratios during the PSAT Math examination. This is a paper-administered test, during which you must fill in your answers on a grid or write them out with a pencil.
There are two sections within the math portion of examination, one which allows you to use a calculator and one which does not. You'll find that the majority of the test questions are multiple choice and the remaining are student-produced response questions.
1. Properties of Shapes: Triangles
Isosceles, equilateral and obtuse, oh my! These are terms for triangles. But, what do they mean? In this lesson, we'll explore the properties of triangles and take a closer look at the different types of triangles you may encounter.
2. 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.
3. 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.
4. Special Right Triangles: Types and Properties
Not all right triangles are the same. In this lesson, we'll look at two special right triangles (30-60-90 and 45-45-90) that have unique properties to help you quickly and easily solve certain triangle problems.
5. Trigonometry: Sine and Cosine
Learn an easy trick to help you solve trigonometry problems, including problems with sine, cosine and inverse trig functions. At the end of this lesson, you'll know what SohCahToa means and how to use it.
6. Trigonometric Ratios and Similarity
Where do terms like sine, cosine and tangent come from? In this lesson, we'll learn about how similarity with right triangles leads to trigonometric ratios.
7. 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.
8. Finding Distance with the Pythagorean Theorem
How much faster is it to cut the corners in a race around the block? In this lesson, review the Pythagorean Theorem, and figure out how to solve without a right triangle.
9. Practice Finding the Trigonometric Ratios
So you know what sine, cosine and tangent are. Great! But how do you use them? Find out how in this lesson as we find missing sides and angles using trigonometric ratios.
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Other chapters within the PSAT Prep: Practice & Study Guide course
- PSAT: About the Test
- PSAT Writing: About the Writing & Language Test
- PSAT Writing: Sentence Clarity and Structure
- PSAT Writing Usage & Punctuation
- Word Use & Expressions in Writing
- Argument & Evidence Analysis in Writing
- About the PSAT Reading Test
- PSAT Reading: Reading Passages
- PSAT Reading: Understanding Reading Passages
- PSAT Reading: Interpretation & Analysis of Text
- Analyzing Data & Graphs in a Reading Passage
- PSAT Reading: Literary Terms
- Important U.S. Documents & Speeches
- Analyzing Words in Context while Reading
- PSAT Math: About the Math Test
- PSAT Math: Numbers and Operations
- PSAT Math: Equations and Expressions
- PSAT Math: Quadratic Equations
- PSAT Math: Exponents
- PSAT Math: Rational Equations and Expressions
- PSAT Math: Inequalities
- PSAT Math: Functions
- PSAT Math: Ratios, Rates & Proportion
- PSAT Math: Geometry and Measurement
- PSAT Math: Data Analysis, Statistics and Probability