# Ch 7: Basic Geometry: Triangles

### About This Chapter

## Who's It For?

Anyone who needs help learning or mastering triangles material will benefit from the lessons in this chapter. There is no faster or easier way to learn about triangles. Among those who would benefit are:

- Students who have fallen behind in understanding triangles
- Students who struggle with learning disabilities or learning differences, including autism and ADHD
- Students who prefer multiple ways of learning math (visual or auditory)
- Students who have missed class time and need to catch up
- Students who need an efficient way to learn about triangles
- Students who struggle to understand their teachers
- Students who attend schools without extra math learning resources

## How It Works:

- Find videos in our course that cover what you need to learn or review.
- Press play and watch the video lesson.
- Refer to the video transcripts to reinforce your learning.
- Test your understanding of each lesson with short quizzes.
- Verify you're ready by completing the Basic Geometry: Triangles chapter exam.

## Why It Works:

**Study Efficiently:**Skip what you know, review what you don't.**Retain What You Learn:**Engaging animations and real-life examples make topics easy to grasp.**Be Ready on Test Day:**Use the Basic Geometry: Triangles chapter exam to be prepared.**Get Extra Support:**Ask our subject-matter experts any triangles question. They're here to help!**Study With Flexibility:**Watch videos on any web-ready device.

## Students Will Review:

This chapter helps students review the concepts in a triangles unit of a standard basic geometry course. Topics covered include:

- Defining and classifying triangles
- Triangle theorems and proofs
- Identifying interior and exterior angles
- Measuring angles
- Defining the medians, altitudes and bisectors of triangles

### 1. Triangles: Definition and Properties

Triangles are shapes with three sides and three angles that lie on a two dimensional plane. Study the definition and properties of triangles including sides and angles, base and height, and opposite and adjacent sides.

### 2. Classifying Triangles by Angles and Sides

Triangles are two-dimensional shapes that have three sides, which can be a variety of lengths to create three angles of varied sizes. Learn how to classify triangles on the basis of their angles and sides, and explore the properties of scalene, isosceles, equilateral, acute, obtuse, and right triangles.

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

A triangle is considered a right triangle when it has a 90-degree angle. Learn the definition and properties of right triangles, and explore relevant proofs and theorems about triangles, such as the Pythagorean theorem and the right triangle altitude theorem.

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

Triangles have interior angles and also exterior angles that are created when an adjacent side of a triangle is extended. Explore the definition and examples of the interior and exterior angles of triangles, learn how to use the properties of triangles and angles to find missing angles, and work practice problems to gain more understanding.

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

When measuring the angles of triangles, it is imperative to remember that all triangles have three angles that add up to 180 degrees. Learn about the three angles in a triangle and how to use a formula to find the measure of a missing angle.

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

In geometry, lines can be added to triangles to help with functions such as computing the area or dividing one triangle into two congruent triangles. Learn about these lines, including the median, altitude, and angle bisector. Review their characteristics, and explore isosceles and equilateral triangles.

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

Triangle congruence postulates of side-side-side (SSS), side-angle side (SAS), or angle-side-angle (ASA) refer to truths about triangles without the need for proof. Explore the SSS, SAS, and ASA triangle congruence postulates in detail and learn how to apply them with provided examples.

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

The AAS Theorem asserts that when two angles and any given side are congruent between two triangles, the triangles are congruent. Explore this concept through practicing an example problem, and demonstrate the proof to find congruence.

### 9. The Sierpinski Triangle & The Chaos Game

This lesson will give an explanation of what the Sierpinski Triangle is and two different ways it can be constructed. We will also look at the connection between the chaos game and the construction of the Sierpinski Triangle.

### Earning College Credit

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### Other Chapters

Other chapters within the Basic Geometry: Help & Review course

- Introduction to Basic Geometry
- Geometry Topics
- Lines and Angles in Geometry
- Basic Geometry: Lines & Angles
- Introduction to Geometric Figures: Help and Review
- Basic Geometry: Polygons
- Basic Geometry: Quadrilaterals
- Basic Geometry: Circles
- Basic Geometric Constructions
- Basic Geometry: Similar Figures
- Basic Geometry: Perimeter, Circumference & Area
- Basic Geometry: 3-Dimensional Figures
- Perimeter, Area & Volume
- Geometric Properties of Objects
- Geometric Graphing Basics
- Geometric Graphing Functions