# 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

A perpendicular bisector is used in geometry theorems, proofs, and constructions. Learn how to create a perpendicular bisector, understand its definition, and and see some real-life examples.

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

An angle bisector is a line that bisects the angle it's drawn from. Study the definition of angle bisector theorem, how to prove it, and examples of this theorem.

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

A parabola is an open curve that is highly distinguishable due to its symmetry along a certain axis. Learn how to write the equation of a parabola in standard form and understand the significance of the vertex and focus of a 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

Inscribed triangles appear with a triangle inside a circle, and circumscribed triangles have a circle inside their boundary. See examples of inscribed and circumscribed triangles, and follow the steps using a ruler and compass to learn to construct both types of triangles correctly.

### 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. Proving the Triangle Midsegment Theorem

The Triangle Midsegment Theorem has many practical uses in real-life. Learn about this theorem and discover its proof to understand how and why it works.

### 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

Pythagorean theorem, named after the mathematician Pythagoras, shows the relation between the sum of the squares of each of the three sides of a right triangle. Learn about the definition of the Pythagorean theorem, discover how a right triangle and sides of a triangle are used in the equation of the theorem, and explore the application of the Pythagorean theorem through relevant examples.

### 11. The Pythagorean Theorem: Practice and Application

Discover how the Pythagorean theorem helps people to solve for all sides of a triangle. Learn about the basics, purpose, and applications of the Pythagorean theorem.

### 12. Special Right Triangles: Types and Properties

There are two types of special right triangles that have either 30-60-90 degree angles or 45-45-90 degree angles. Learn more about the definitions and explore the properties of 30-60-90 and 45-45-90 degree angles of special right triangles through examples.

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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