# Ch 35: NES Math: Properties of Triangles

### About This Chapter

## NES Math: Properties of Triangles - Chapter Summary

Refresh your understanding of triangles and re-discover how to measure their areas and angles through these lively lessons. Our study aids will help you get ready for NES Math test questions on the following topics:

- Definition and properties and triangles
- How to find the area of triangles and rectangles
- Ways to classify triangles by sides and angles
- Methods of determining perimeter of rectangles and triangles
- Altitude, median and angle bisectors of a triangle
- Dilation, concurrent lines and right triangle theorems
- The Pythagorean theorem

These lessons are available anytime, via computer or mobile device. They average about five minutes each and are packed with examples, humor and insightful explanations that make them informative and fun. You can contact the instructors if you have questions and track your studies through our online Dashboard.

### NES Math: Properties of Triangles Chapter Objectives

In several states, passing the NES Math test is one of the requirements for obtaining certification to teach math at the secondary school level. The test consists entirely of multiple-choice questions, divided into five contest domains. Worth 19% of the exam score, the Measurement and Geometry content domain includes questions on material described in the Properties of Triangles chapter. You can get good experience answering questions in the format found on the NES test by completing the quizzes and the chapter exam in our study guide.

### 1. Triangles: Definition and Properties

What makes a shape a triangle? In this lesson, we'll explore the definition of a triangle, then analyze the parts of triangles, including the vertices, base and height.

### 2. Area of Triangles and Rectangles

How do you find out the area of rectangles and triangles? Learn how in this lesson! We'll look at the formulas, then practice solving problems for each shape.

### 3. Classifying Triangles by Angles and Sides

Not all triangles are the same. There are equilateral, isosceles and scalene triangles. Then there are right, acute and obtuse triangles. In this lesson, we'll learn how to classify triangles using their sides and angles.

### 4. Perimeter of Triangles and Rectangles

Without realizing it, we calculate and use the perimeter of triangles and rectangles in regular everyday situations. Learn more about the perimeter of triangles and rectangles in this lesson, and test your knowledge with a quiz.

### 5. Interior and Exterior Angles of Triangles: Definition & Examples

Knowing just a few things about the interior or exterior angles of triangles is sometimes all you need to put all the pieces together. Find out more in this lesson.

### 6. 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.

### 7. Median, Altitude, and Angle Bisectors of a Triangle

Line segments in triangles are just clutter; they have special names and qualities depending on how they're drawn. In this lesson, we'll learn about medians, altitudes and angle bisectors.

### 8. Properties of Concurrent Lines in a Triangle

Centroids, orthocenters, incenters, circumcenters, oh my! Don't worry though. In this lesson, we master the various terms for concurrent lines in triangles and match them to altitudes, angle bisectors, perpendicular bisectors and medians.

### 9. Dilation in Math: Definition & Meaning

Dilations are transformations that change figures in specific ways. Learn about these changes and how to complete dilations here. Then test your understanding with a quiz.

### 10. Properties of Right Triangles: Theorems & Proofs

In this lesson, you will learn about the properties of and theorems associated with right triangles, which have a wide range of applications in math and science. Specifically, we will discuss and prove the Pythagorean theorem and the right triangle altitude theorem. Let's get started.

### 11. 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.

### 12. The Pythagorean Theorem: Converse and Special Cases

The Pythagorean Theorem is a famous theorem for right triangles. Watch this video to learn how the Pythagorean Theorem relates to the law of cosines and how the converse of the Pythagorean Theorem can help you identify right triangles.

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### Other Chapters

Other chapters within the NES Mathematics (304): Practice & Study Guide course

- NES Math: Properties of Real Numbers
- NES Math: Fractions
- NES Math: Decimals & Percents
- NES Math: Ratios & Proportions
- NES Math: Units of Measure & Conversions
- NES Math: Logic
- NES Math: Reasoning
- NES Math: Vector Operations
- NES Math: Matrix Operations & Determinants
- NES Math: Exponents & Exponential Expressions
- NES Math: Algebraic Expressions
- NES Math: Linear Equations
- NES Math: Inequalities
- NES Math: Absolute Value
- NES Math: Quadratic Equations
- NES Math: Polynomials
- NES Math: Rational Expressions
- NES Math: Radical Expressions
- NES Math: Systems of Equations
- NES Math: Complex Numbers
- NES Math: Functions
- NES Math: Piecewise Functions
- NES Math: Exponential & Logarithmic Functions
- NES Math: Continuity of Functions
- NES Math: Limits
- NES Math: Rate of Change
- NES Math: Derivative Rules
- NES Math: Graphing Derivatives
- NES Math: Applications of Derivatives
- NES Math: Area Under the Curve & Integrals
- NES Math: Integration Techniques
- NES Math: Applications of Integration
- NES Math: Foundations of Geometry
- NES Math: Geometric Figures
- NES Math: Triangle Theorems & Proofs
- NES Math: Parallel Lines & Polygons
- NES Math: Quadrilaterals
- NES Math: Circles & Arc of a Circle
- NES Math: Conic Sections
- NES Math: Geometric Solids
- NES Math: Analytical Geometry
- NES Math: Trigonometric Functions
- NES Math: Trigonometric Graphs
- NES Math: Solving Trigonometric Equations
- NES Math: Trigonometric Identities
- NES Math: Sequences & Series
- NES Math: Graph Theory
- NES Math: Set Theory
- NES Math: Statistics Overview
- NES Math: Summarizing Data
- NES Math: Tables, Plots & Graphs
- NES Math: Probability
- NES Math: Discrete Probability Distributions
- NES Math: Continuous Probability Distributions
- NES Math: Sampling
- NES Math: Regression & Correlation
- NES Mathematics Flashcards