# Ch 22: High School Algebra: Measurement and Geometry

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### About This Chapter

## Measurement and Geometry - Chapter Summary and Learning Objectives

In this chapter, the instructor will teach you basic concepts when using standard units of measurement for various types of shapes. By the time you complete this chapter, you will know how to subtract, multiply, add and divide measurements. These lessons can help you understand how to:

- Calculate the area of triangles, rectangles and circles
- Convert metric units of measurement
- Define different types of angles
- Identify various line types
- Apply the Pythagorean theorem
- Explain the properties of shapes

Video | Objective |
---|---|

Standard Units of Measure | Explain the standard units of measure, including units of length, weight, time and capacity. |

How to Convert Standard Units of Measure | Explain how to convert one unit of measurement to another using the conversion factor. |

How to Perform Basic Operations with Measurements | Explain how to add, subtract, multiply and divide measurements. |

What is the Metric System? | Define the metric system and its basic measures of length, weight and liquid capacity. |

How to Convert Units in the Metric System | Explain the steps in changing metric units. |

How to Read and Interpret Scales and Meters | Describe scenarios in which one would encounter scale drawings and meters. Explain how to read and interpret information on scales and meters. |

Points, Lines and Angles in Geometry | Define basic vocabulary surrounding geometry, including point, types of lines, degrees and right angles. |

Types of Angles: Vertical, Corresponding, Alternate Interior and Others | Learn the definitions of vertical angles, corresponding angles, alternate interior angles, alternate exterior angles and consecutive interior angles. |

Parallel, Perpendicular and Transverse Lines | Learn the definitions of parallel, perpendicular and transversal lines. |

Shapes and Geometry | Describe the basic shapes found in geometry, including triangles, polygons, quadrilaterals, parallelograms, rectangles, squares, trapezoids, pentagons, octagons and circles. |

Properties of Shapes: Triangles, Circles and Rectangles | Describe the properties of triangles, circles and rectangles. |

Perimeter of Triangles and Rectangles | Calculate the perimeter of triangles and rectangles. |

Area of Triangles and Rectangles | Calculate the area of triangles, circles and rectangles |

Circles: Area and Circumference | Calculate the area and circumference of circles |

The Pythagorean Theorem: Practice and Application | Learn the Pythagorean theorem and practice its real-life application. |

How to Identify Similar Triangles | Learn how to identify similar triangles. |

Applications of Similar Triangles | Learn how to solve applications of similar triangles. |

Angles and Triangles: Practice Problems | Get practice solving for angles and triangles. |

Angular Relationships and Special Pairs of Angles | Explain how to use special angular relationships (complementary and vertical) to find the measure of angles whose number is unknown. |

Three-dimensional Figures in Geometry | Describe three-dimensional figures in geometry, including solids, rectangular solids, cubes, cylinders and spheres. |

How to Measure Volume | Explain how to measure the volume of a three-dimensional figure. |

### 1. Standard Units of Measurement for Length, Weight, Time & Capacity

Watch this video lesson to learn how to recognize the various units of measurement for length, weight, time and volume. Learn to recognize both U.S. units and metric units.

### 2. How to Convert Standard Units of Measure

The United States uses pounds, miles and Fahrenheit for measurements, but the rest of the world uses the metric system. This video lesson will help you to convert from one to the other easily, so you can understand kilometers and kilograms, too.

### 3. How to Perform Basic Operations with Measurements

In this video lesson, you will learn how measurements are very much like variables when it comes to adding, subtracting, multiplying, and dividing them. You will also see examples of how they are done.

### 4. What is the Metric System?

Most of the world relies on the metric system for measuring distance, weight, volume, and time. Watch this video lesson to learn what kinds of measurements are used in the metric system.

### 5. How to Convert Units in the Metric System

If you can make dinner, you can convert units in the metric system. It's that easy! In this lesson, you'll learn about the three key things you'll need to perform conversions.

### 6. How to Take Measurements with Scales, Meters & Gauges

In the real world, we take measurements all the time. Measurements are taken when you drive and when you weigh yourself, for example. Watch this video lesson to learn how you can take measurements of things that are important.

### 7. How to Read and Interpret Scale Drawings

Watch this video lesson to learn how scale drawings and legends are used on maps and blueprints. Learn skills that will serve you well when traveling and when looking at the blueprints of a car.

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

After watching this video lesson, you should understand the basic terms that form the foundation of geometry. Learn what a point is, what a line is, what an angle is, and learn about a special type of angle called a right angle.

### 9. Types of Angles: Vertical, Corresponding, Alternate Interior & Others

In addition to basic right, acute, or obtuse angles, there are many other types of angles or angle relationships. In this lesson, we will learn to identify these angle relationships and discuss their measurements.

### 10. Overview of the Basic Shapes in Geometry

Watch this video lesson to learn about some basic shapes in geometry. These are the shapes that you will come across most often in math. Watch as triangles, rectangles, pentagons, and circles come by.

### 11. Properties of Shapes: Rectangles, Squares and Rhombuses

What's the difference between a square and a rectangle? What about a rhombus and a square? In this lesson, we'll look at the properties of these shapes.

### 12. Properties of Shapes: Triangles

Isosceles, equilateral and obtuse, oh my! These are terms for triangles. But, what do they mean? In this lesson, we'll explore the properties of triangles and take a closer look at the different types of triangles you may encounter.

### 13. Perimeter of Triangles and Rectangles

Without realizing it, we calculate and use the perimeter of triangles and rectangles in regular everyday situations. Learn more about the perimeter of triangles and rectangles in this lesson, and test your knowledge with a quiz.

### 14. Area of Triangles and Rectangles

How do you find out the area of rectangles and triangles? Learn how in this lesson! We'll look at the formulas, then practice solving problems for each shape.

### 15. Circles: Area and Circumference

Understanding how to calculate the area and circumference of circles plays a vital role in some of our everyday functions. They serve as the foundation for operating with three-dimensional figures. Learn more about the area and circumference of circles in this lesson.

### 16. 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.

### 17. How to Identify Similar Triangles

Similar triangles have the same characteristics as similar figures but can be identified much more easily. Learn the shortcuts for identifying similar triangles here and test your ability with a quiz.

### 18. Applications of Similar Triangles

Similar triangles are used to solve problems in everyday situations. Learn how to solve with similar triangles here, and then test your understanding with a quiz.

### 19. Angles and Triangles: Practice Problems

Want more practice solving with angle pairs? How about more review for solving angles in triangles? Look no further. Get more practice here, and test your ability with a quiz.

### 20. Vertical Angles & Complementary Angles: Definition & Examples

Special angles make your life easier. Learn how you can use the properties of special angles to help you find the measurements of missing angles in this video lesson.

### 21. Overview of Three-dimensional Shapes in Geometry

We are surrounded by three-dimensional shapes. Watch this video lesson to see what some three-dimensional shapes look like, such as a cube, a sphere, a brick, and a cylinder.

### 22. How to Calculate the Volumes of Basic Shapes

Squares pegs = square holes. Triangular pegs = triangular holes. But where does a sphere go? In this lesson, review volumes of common shapes while contrasting a sphere and a cylinder - after all, they both go into the circular hole... right?

### 23. Volume of Cylinders, Cones, and Spheres

In this lesson, we'll learn about the volume formulas for cylinders, cones and spheres. We'll also practice using the formula in a variety of real-world examples where knowing how to calculate volume is helpful.

### 24. Volume of Prisms and Pyramids

In this lesson, we'll learn about prisms and pyramids. We'll look at the different types of prisms and pyramids, as well as practice calculating volume for each shape.

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### Other Chapters

Other chapters within the Remedial Algebra I course

- High School Algebra: Basic Arithmetic
- High School Algebra: Solving Math Word Problems
- High School Algebra: Decimals and Fractions
- High School Algebra: Percent Notation
- High School Algebra: Real Numbers
- High School Algebra: Exponents and Exponential Expressions
- High School Algebra: Radical Expressions
- High School Algebra: Algebraic Expressions and Equations
- High School Algebra: Properties of Functions
- High School Algebra: Matrices and Absolute Value
- High School Algebra: Working With Inequalities
- High School Algebra: Properties of Exponents
- High School Algebra: Complex and Imaginary Numbers
- High School Algebra: Algebraic Distribution
- High School Algebra: Linear Equations
- High School Algebra: Factoring
- High School Algebra: Graphing and Factoring Quadratic Equations
- High School Algebra: Properties of Polynomial Functions
- High School Algebra: Rational Expressions
- High School Algebra: Cubic Equations
- High School Algebra: Quadratic Equations
- High School Algebra: Calculations, Ratios, Percent & Proportions
- High School Algebra: Data, Statistics, and Probability
- High School Algebra: Well-Known Equations