# Ch 1: Explorations in Core Math Geometry Chapter 1: Foundations for Geometry

### About This Chapter

## How It Works:

- Find the lesson within this chapter that corresponds to what you're studying in the Foundations for Geometry chapter of your textbook.
- Watch fun videos that cover the basic geometry 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:

- The definition of line segments, points and angles
- The midpoint theorem
- Constructing circles
- Measuring angles
- Geometry formulas
- Finding the distance between points
- Transformations

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

### 1. Points, Lines & Angles in Geometry

Geometry is a sector of mathematics that analyzes shapes, lines, and surfaces. Explore the definitions and examples of the basics of geometry: points, lines, and angles.

### 2. Line Segments & Rays: Definition & Measurement

A line segment is a line with a starting point and endpoint, while a ray is a line with only one endpoint. Learn the definition of line segments and rays, how the distance of line segments is used in measurements, and discover how to add line segments together.

### 3. Line Segment Bisection & Midpoint Theorem: Geometric Construction

A line segment is a line with a beginning and an end. In this lesson, the reader will explore the midpoint theorem, that helps you calculate the midpoint of the line segment, how to use geometric construction where you don't know the location of the points of the line segment, and how to bisect a line segment.

### 4. Geometric Constructions Using Lines and Angles

It is possible to construct different geometric shapes and patterns using lines and angles. Explore the definition of geometric construction, the tools required for the job, and how to copy angles and line segments.

### 5. How to Construct a Circle With a Compass

Circles are easy to create with the use of a compass. Learn about the compass and discover how to construct a circle with a compass step-by-step with examples.

### 6. How to Measure Angles with a Protractor

A protractor is a measuring tool for angles and can also be used to draw angles. Learn about vocabulary related to angles and protractors, the different types of angles, and understand how to measure and draw angles.

### 7. Constructing an Angle Bisector in Geometry

In geometry, an angle bisector is a line that splits an angle exactly in half. Learn the method of geometric construction, including the process for constructing an angle bisector.

### 8. Angle Pairs: Types & Concept

In geometry, there are five major categories of angles. Learn the types and concept of the following angle pairs: complementary angles, linear pairs, supplementary angles, vertical angles, and adjacent angles.

### 9. Using & Rewriting Formulas in Geometry

There are lots of formulas in geometry. They can help you find area, surface area and volumes, and other quantities for geometric figures. In this lesson you will learn how to use geometry formulas, and you will look at how to rewrite formulas to answer questions about geometric figures.

### 10. How to Find the Distance Between Two Points

The distance between two points on a coordinate plane tells us how far apart the objects are from one another. Learn how to find this distance using the distance formula and some step-by-step examples.

### 11. How to Use The Midpoint Formula

The midpoint formula enables us to find the midpoint of a line segment when we know the endpoints. Learn about line segments, midpoints, and how to use the midpoint formula. Explore examples, and understand that the midpoint can be found on both vertical and horizontal line segments.

### 12. How to Use The Distance Formula

The distance formula is a shortened form of the Pythagorean Theorem. Learn about the Pythagorean Theorem and the distance formula, along with examples of how the formula is used.

### 13. Transformations: How to Shift Graphs on a Plane

Transformations in mathematics are functions that change into different functions. Explore the different types of transformations including rotations, reflections, dilations, and translations, and learn how to shift graphs on a plane.

### 14. Transformations in Math: Definition & Graph

The movement of objects in the coordinate plane is referred to as transformation. Learn about the different types of transformations, their graphical representations, their application in a coordinate plane, and problem-solving involving transformations.

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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 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 5: Properties and Attributes of Triangles
- 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