# Ch 4: Saxon Calculus: Geometry

### About This Chapter

## How It Works:

- Find the lesson within this chapter that corresponds to what you're studying in the Geometry chapter of your textbook.
- Watch fun videos that cover the calculus and 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 calculus and geometry topics covered in the textbook chapter, including:

- Using the midpoint and distance formulas
- Graphing linear equations using standard and point-slope formulas
- Explanation and illustration of the Pythagorean theorem
- Identification and applications of similar triangles
- Definition of translation and reflection in math
- How to graph tangents and slopes

*Saxon is a registered trademark of Houghton Mifflin Harcourt, which is not affiliated with Study.com.*

### 1. 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.

### 2. 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.

### 3. Linear Equations: Intercepts, Standard Form and Graphing

To solve a linear equation, begin by determining whether it is written in the standard form or the slope-intercept form. Explore the differences between the slope-intercept form and the standard form of a linear equation, and learn how to graph the point of intercept for each.

### 4. Equation of a Line Using Point-Slope Formula

The point-slope formula is composed of a specific point of coordinates and a slope indicating a type of change over a given variable, such as distance over time. Identify the use of point-slope formula in graphing a line through provided examples.

### 5. 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.

### 6. How to Identify Similar Triangles

Similar triangles are defined as two triangles that possess proportional corresponding sides and congruent corresponding angles. Triangle similarity theorems use angle and side comparisons to determine whether two triangles are similar. Learn about the language of similarity, triangle similarity theorems (Angle-Angle, Side-Angle-Side, & Side-Side-Side), and how to use theorems to identify similar triangles.

### 7. Applications of Similar Triangles

Similar triangles have the same shape but differ in size. Learn about the applications of similar triangles, including how to use them and how to solve real-world problems with similar triangles.

### 8. What is Translation in Math? - Definition, Examples, & Terms

An object may be relocated in a coordinate plane by changing the coordinates of the points in an object while retaining the original shape of the object. Learn about the process of translation in mathematics and how it is done on geometric shapes and figures.

### 9. Reflections in Math: Definition & Overview

When an object is reflected in math, it is flipped across a line. Explore the definition of reflections, what transformations are, how to draw reflections, and the overview of reflections in this lesson.

### 10. Slopes and Tangents on a Graph

In mathematics, slopes and tangents help determine ratios and rates of change. Learn how to show slopes and tangents as lines on a graph, explore the concept of slope as it pertains to hills, and recognize how slope can be used to describe steepness.

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### Other Chapters

Other chapters within the Saxon Calculus Homeschool: Online Textbook Help course

- Saxon Calculus: Real Numbers
- Saxon Calculus: Algebra
- Saxon Calculus: Algebra Theorems
- Saxon Calculus: Logic
- Saxon Calculus: Trigonometry
- Saxon Calculus: Graphing Calculator
- Saxon Calculus: Basics of Functions
- Saxon Calculus: Graphing Functions & Equations
- Saxon Calculus: Analysis of Graphs
- Saxon Calculus: Limits of Functions
- Saxon Calculus: Asymptotic & Unbounded Behavior
- Saxon Calculus: Continuity as a Property of Functions
- Saxon Calculus: Parametric, Polar & Vector Functions
- Saxon Calculus: Concept of the Derivative
- Saxon Calculus: Derivative at a Point
- Saxon Calculus: Derivative as a Function
- Saxon Calculus: Second Derivatives
- Saxon Calculus: Applications of the Derivative
- Saxon Calculus: Computation of Derivatives
- Saxon Calculus: Riemann Sums
- Saxon Calculus: Interpretations & Properties of Definite Integrals
- Saxon Calculus: Applications of Integrals
- Saxon Calculus: Fundamental Theorem of Calculus
- Saxon Calculus: Techniques of Antidifferentiation
- Saxon Calculus: Applications of Antidifferentiation
- Saxon Calculus: Numerical Approximation of Definite Integrals
- Saxon Calculus: Concept of Series
- Saxon Calculus: Series of Constants
- Saxon Calculus: Taylor Series