# Ch 5: Explorations in Core Math Geometry Chapter 5: Properties and Attributes of Triangles

### About This Chapter

## How It Works:

- Find the lesson within this chapter that corresponds to what you're studying in the Properties and Attributes of Triangles chapter of your textbook.
- Watch fun videos that cover the triangle concepts you need to learn or review.
- Complete the quiz after watching each video lesson to test your understanding.
- If you need additional help, rewatch the videos until you've mastered the material, or submit a question for one of our instructors.

## Chapter Topics

You'll learn all of the geometry topics covered in the textbook chapter, including:

- What a perpendicular bisector is
- The angle bisector theorem
- Standard form for writing parabola equations
- Constructing circumscribed and inscribed triangles
- The triangle midsegments theorem
- Inequalities in triangles
- The Pythagorean theorem
- Properties of special right triangles

*Explorations in Core Math is a registered trademark of Houghton Mifflin Harcourt, which is not affiliated with Study.com.*

### 1. Perpendicular Bisector: Definition, Theorem & Equation

How can we draw a triangle that will have two exactly equal length sides? Or what if we need to find the center of a circle that passes through a given set of points? In this lesson, we'll learn about the perpendicular bisector and how useful it can be in geometry!

### 2. Angle Bisector Theorem: Proof and Example

The angle bisector theorem sounds almost too good to be true. In this lesson, we set out to prove the theorem and then look at a few examples of how it's used.

### 3. How to Write the Equation of a Parabola in Standard Form

After watching this video lesson, you will be able to write the equation of a parabola in standard form when given just two important points from the parabola. Learn what these two points are and how they relate to the parabola.

### 4. How to Draw Circumscribed & Inscribed Circles

Drawing accurate circumscribed or inscribed circles can be a tricky process. In this lesson, we'll explore the process for drawing perfect inscribed and circumscribed circle for any polygon where it's possible.

### 5. Constructing Inscribed & Circumscribed Triangles

View this lesson to learn how you can construct inscribed and circumscribed triangles. Learn how both involve circles. All you need are a ruler and a compass.

### 6. 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.

### 7. Proving the Triangle Midsegments Theorem

The Triangle Midsegment Theorem is extremely useful in real-world applications. This lesson will state the Triangle Midsegment Theorem, apply it to an example, and then provide a proof of the theorem.

### 8. Proving Angle-Side Relationships in Triangles

In this lesson you'll learn how to use inequalities to relate the angles and sides of triangles and how to use and write an indirect proof. You'll also learn how to apply the hinge theorem when solving geometry problems.

### 9. Inequalities in Triangles

What do you know about the relationship between side length and angle measure in triangles? Keep reading and we'll cover the relationship between two given side lengths of a triangle and its third side length and the relationship between the side lengths of triangles and their angle measures.

### 10. Pythagorean Theorem: Definition & Example

Learn what the Pythagorean Theorem says about a right triangle and the relationships of its three sides to each other by watching this video lesson. Also learn how you can use this to your advantage when solving problems.

### 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. 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.

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### Other Chapters

Other chapters within the Explorations in Core Math - Geometry: Online Textbook Help course

- Explorations in Core Math Geometry Chapter 1: Foundations for Geometry
- Explorations in Core Math Geometry Chapter 2: Geometric Reasoning
- Explorations in Core Math Geometry Chapter 3: Parallel and Perpendicular Lines
- Explorations in Core Math Geometry Chapter 4: Triangle Congruence
- Explorations in Core Math Geometry Chapter 6: Polygons and Quadrilaterals
- Explorations in Core Math Geometry Chapter 7: Similarity
- Explorations in Core Math Geometry Chapter 8: Right Triangles and Trigonometry
- Explorations in Core Math Geometry Chapter 9: Extending Transformational Geometry
- Explorations in Core Math Geometry Chapter 10: Extending Perimeter, Circumference and Area
- Explorations in Core Math Geometry Chapter 11: Spatial Reasoning
- Explorations in Core Math Geometry Chapter 12: Circles
- Explorations in Core Math Geometry Chapter 13: Probablity