OML Search

The Pythagorean Theorem





 


Videos to help Grade 8 students learn that when the square of a side of a right triangle represented as a2, b2 or c2 is not a perfect square, they can estimate the side length as between two integers and identify the integer to which the length is closest.

New York State Common Core Math Grade 8, Module 7, Lesson 1.

Related Topics:
Lesson Plans and Worksheets for Grade 8

Lesson Plans and Worksheets for all Grades

More Lessons for Grade 8

Common Core For Grade 8

Lesson 1 Summary

Perfect square numbers are those that are a product of an integer factor multiplied by itself. For example, the number 25 is a perfect square number because it is the product of multiplied 5 by 5.

When the square of the length of an unknown side of a right triangle is not equal to a perfect square, you can estimate the length by determining which two perfect squares the number is between.


Lesson 1 Classwork

Show students the three triangles below.
The first triangle requires students to use the Pythagorean Theorem to determine that the unknown side length.
The second triangle requires students to use the converse of the theorem to determine that it is a right triangle.
The third triangle requires students to use the converse of the theorem to determine that it is not a right triangle.

Recall the Pythagorean Theorem and its converse for right triangles.
• The Pythagorean Theorem states that a right triangle with leg lengths a and b and hypotenuse c will satisfy a2 + b2 = c2.
The converse of the theorem states that if a triangle with side lengths a, b, and c satisfy the equation a2 + b2 = c2, then the triangle is a right triangle.

Example 1 - Example 3
Write an equation that will allow you to determine the length of the unknown side of the right triangle.
Example 4
In the figure below, we have an equilateral triangle with a height of 10 inches. What do we know about an equilateral triangle?
Exercises 1–3
1. Use the Pythagorean Theorem to estimate the length of the unknown side of the right triangle. Explain why your estimate makes sense.





Rotate to landscape screen format on a mobile phone or small tablet to use the Mathway widget, a free math problem solver that answers your questions with step-by-step explanations.


You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.



OML Search


We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.


[?] Subscribe To This Site

XML RSS
follow us in feedly
Add to My Yahoo!
Add to My MSN
Subscribe with Bloglines