# Ch 32: Praxis Middle School Math: Properties of Triangles

### About This Chapter

## Praxis Middle School Math: Properties of Triangles - Chapter Summary

As you study for the Praxis Middle School Mathematics exam, this chapter will provide a resource for developing your knowledge of triangles. These lessons will explain the basic properties of triangles and will detail the following topics that will enhance your abilities to answer any triangle-related questions on the exam:

- Angle-angle-side theorem and other triangle congruency postulates
- Congruency of isosceles and right triangles
- Properties of concurrent lines in a triangle
- Equilateral and right triangles and their properties
- Median, altitude, and angle bisectors of a triangle
- Measuring a triangle's angles

These lessons present the information to you in the form of short, creatively animated videos. If that is not the method you learn best with, read the accompanying full transcription. Should you need further assistance with any of the topics, submit your request to our experts and they will reply as soon as they are able.

### 1. The AAS (Angle-Angle-Side) Theorem: Proof and Examples

When trying to find out if triangles are congruent, it's helpful to have as many tools as possible. In this lesson, we'll add to our congruence toolbox by learning about the AAS theorem, or angle-angle-side.

### 2. Triangle Congruence Postulates: SAS, ASA & SSS

When we have two triangles, how can we tell if they're congruent? They may look the same, but you can be certain by using one of several triangle congruence postulates, such as SSS, SAS or ASA.

### 3. Congruency of Isosceles Triangles: Proving the Theorem

Isosceles triangles have two equal sides. Are the base angles also equal? In this lesson, we'll prove how this is true. We'll also prove the theorem's converse.

### 4. 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.

### 5. 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.

### 6. What is an Equilateral Triangle? - Definition, Properties & Formula

In this lesson, you'll discover what equilateral triangles are and the properties they have that make them unique. You'll also learn two formulas that are associated with equilateral triangles. Then, you can test your knowledge with a brief 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 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.

### 9. Congruency of Right Triangles: Definition of LA and LL Theorems

In this lesson, we'll learn two theorems that help us prove when two right triangles are congruent to one another. The LA theorem, or leg-acute, and LL theorem, or leg-leg, are useful shortcuts for proving congruence.

### 10. Measuring the Angles of Triangles: 180 Degrees

Watch this video lesson to see why a triangle's angles always add up to 180 degrees. Also, learn how you can use this unique fact about triangles to find an unknown angle in a triangle.

### 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

Other chapters within the Praxis Middle School Mathematics (5169): Practice & Study Guide course

- Praxis Middle School Math: Number Basics
- Praxis Middle School Math: Rational Numbers
- Praxis Middle School Math: Properties of Numbers
- Praxis Middle School Math: Number Structure
- Praxis Middle School Math: Absolute Value
- Praxis Middle School Math: Equality
- Praxis Middle School Math: Arithmetic Operations
- Praxis Middle School Math: Introduction to Fractions
- Praxis Middle School Math: Operations with Fractions
- Praxis Middle School Math: Decimals
- Praxis Middle School Math: Percents
- Praxis Middle School Math: Ratios & Rate of Change
- Praxis Middle School Math: Proportional Relationships
- Praxis Middle School Math: Estimation
- Praxis Middle School Math: Scientific Notation & Exponents
- Praxis Middle School Math: Square Roots
- Praxis Middle School Math: Roots & Radicals
- Praxis Middle School Math: Algebra Basics
- Praxis Middle School Math: Principles of Algebra
- Praxis Middle School Math: Solving Word Problems
- Praxis Middle School Math: Functions
- Praxis Middle School Math: Linear Equations
- Praxis Middle School Math: Solving Linear Equations
- Praxis Middle School Math: Patterns in Math
- Praxis Middle School Math: Graphing Functions
- Praxis Middle School Math: Polynomials
- Praxis Middle School Math: Quadratic Equations
- Praxis Middle School Math: Systems of Equations
- Praxis Middle School Math: Area, Perimeter & Volume
- Praxis Middle School Math: Properties & Theorems
- Praxis Middle School Math: Parallel, Perpendicular & Intersecting Lines
- Praxis Middle School Math: Similarity & Congruence
- Praxis Middle School Math: Quadrilaterals
- Praxis Middle School Math: Polygons
- Praxis Middle School Math: Circles
- Praxis Middle School Math: Coordinate Geometry
- Praxis Middle School Math: Measurement
- Praxis Middle School Math: Geometric Construction
- Praxis Middle School Math: Data
- Praxis Middle School Math: Line Graphs
- Praxis Middle School Math: Data Presentation
- Praxis Middle School Math: Probability
- Praxis Middle School Math: Logic
- Praxis Middle School Math: Modeling
- Praxis Middle School Mathematics Flashcards