About This Chapter
Who's It For?
Anyone who needs help learning or mastering triangle material will benefit from the lessons in this chapter. There is no faster or easier way to learn about triangles. Among those who would benefit are:
- Students who have fallen behind in understanding the formulas and properties of triangles
- Students who struggle with learning disabilities or learning differences, including autism and ADHD
- Students who prefer multiple ways of learning math (visual or auditory)
- Students who have missed class time and need to catch up
- Students who need an efficient way to learn about triangles
- Students who struggle to understand their teachers
- Students who attend schools without extra math learning resources
How It Works:
- Find videos in our course that cover what you need to learn or review.
- Press play and watch the video lesson.
- Refer to the video transcripts to reinforce your learning.
- Test your understanding of each lesson with short quizzes.
- Verify you're ready by completing the ACT Math - Triangles chapter exam.
Why It Works:
- Study Efficiently: Skip what you know, review what you don't.
- Retain What You Learn: Engaging animations and real-life examples make topics easy to grasp.
- Be Ready on Test Day: Use the ACT Math - Triangles chapter exam to be prepared.
- Get Extra Support: Ask our subject-matter experts any question about triangles. They're here to help!
- Study With Flexibility: Watch videos on any web-ready device.
Students Will Review:
This chapter helps students review the concepts in a triangles unit of a standard ACT Prep course. Topics covered include:
- Properties of triangles
- Determining the perimeter and area of triangles and rectangles
- Using the Pythagorean Theorem to find distance
- Identifying and applications of similar triangles
- Types and properties of special right triangles and 3-4-5 triangles
1. Properties of Shapes: Triangles
Triangles are three-sided shapes with three angles. Learn the basic properties of triangles, explore the types identified by their sides and angles and types classified by angles alone, and understand different combinations for naming triangles.
2. Perimeter of Triangles and Rectangles
Perimeter is defined as the combined distance around a shape, object, or figure, while the perimeter of any polygon can be determined by adding the length of all sides. Learn about perimeter, how to use mathematical formulas to calculate the perimeter of triangles and rectangles, and how to use perimeter to determine the length of unknown polygon sides.
3. Area of Triangles and Rectangles
The area of a two-dimensional shape represents the space covered within its perimeter, but area calculations change depending on the shape. Learn how to calculate and solve the areas of right triangles, oblique triangles, and rectangles.
4. Finding Distance with the Pythagorean Theorem
The Pythagorean theorem outlines principles for right triangles, but it can also be used to calculate distance between points. Learn how this theorem is applied to practical examples of ice cream, skateboard ramps, and even the cliff-peak in 'The Lion King.'
5. 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.
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. 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.
8. 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.
9. Properties of 3-4-5 Triangles: Definition and Uses
3-4-5 triangles are special types of triangles that can be run through the Pythagorean theorem to solve. In this lesson, look at the definition, properties, and uses of 3-4-5 triangles, as well as the Pythagorean theorem, Pythagorean triples, 3-4-5 multiples, and how to use 3-4-5 triangles.
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