About This Chapter
In our series of lessons, you'll learn about the properties, areas, and perimeters of basic geometric shapes, such as triangles, circles, and rectangles. You'll learn the properties of these shapes and how you can identify them. For instance, you'll determine that a triangle is a polygon with three sides, while a rectangle is a quadrilateral with four sides joined at 90 degree angles. To help you discern the differences of these shape properties, we'll define terminology, such as vertex, radius, diameter, polygon, angle, right angle, acute angle, obtuse angle, equilateral triangle, scalene triangle, isosceles triangle, altitude, base, and plane.
Once you understand the basic properties of these shapes, you'll study their perimeters (the lines that outline the shapes), as well as their areas (the amount of space within the shapes).
Continuing on with triangles, you'll study the Pythagorean theorem, a theorem used to calculate the length of a triangle's side. You may even recognize this easy-to-remember equation: a^2 + b^2 = c^2. In other words, side a squared plus side b squared equals side c squared, which is the longest side, also known as the hypotenuse. After learning the Pythagorean theorem, you'll solve plenty of practice problems and learn some real-life applications of the theorem.
So, if your skills can use some sharpening, these video lessons can help you get back into shape. Thanks for watching!
1. 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.
2. 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.
3. 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.
4. 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.
5. 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.
6. 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.
7. 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.
8. 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.
9. Parallel, Perpendicular and Transverse Lines
What are the different types of lines? Where are they visible in the real world and how can you recognize them? Find out here and test your knowledge with a quiz.
10. 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.
11. 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.
12. Properties of Shapes: Circles
Circles are fundamental to everything we do. But, did you know they're much more than just round shapes? In this lesson, we'll look at the various parts of circles and how they all relate.
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Other chapters within the Math 102: College Mathematics course
- Math Foundations
- Linear Equations
- Solving and Graphing Inequalities
- Graphing and Factoring Quadratic Equations
- Complex and Imaginary Numbers
- Properties of Exponents
- Properties of Polynomials
- Simplifying and Solving Rational Expressions
- Properties of Functions
- Logarithms and Exponential Equations
- Probability and Statistics