Pythagorean Identity - 2.6.5
Let's Review Pythagorean Theorem
In a previous class you learned about the Pythagorean Theorem, which states that for any right triangle with legs a and b and hypotenuse c, . If you need a refresher, watch the video below:
Task 1:
Write a mathematical statement about the relationship between the sides of the right triangle below:
Task 2:
Plot a point 
in quadrant I on the circumference of Circle O. Rename the point H by right clicking on the point and clicking on "rename".
Construct a perpendicular line 
from point H to the x-axis. Create a point at the intersection of the perpendicular lines 
and label it J.
.
in quadrant I on the circumference of Circle O. Rename the point H by right clicking on the point and clicking on "rename".
Construct a perpendicular line from point H to the x-axis. Create a point at the intersection of the perpendicular lines and label it J.
Construct right triangle HJO .Task 3:
Notice how you can move point H around in Quadrant I. What is the length of the hypotenuse, no matter where you drag point H? For a hint, type "Give me a hint!" and click "check my answer"
Task 4:
Let's call . Define the length of the horizontal leg of triangle in terms of . For a hint, type "Give me a hint!" and click "check my answer"
Task 5:
Define the length of the vertical leg of triangle in terms of . For a hint, type "Give me a hint!" and click "check my answer"
Task 6:
Label the lengths you defined in tasks 3-5 on the triangle below:
Task 7:
Using what we know about Pythagorean Theorem, what can we say about the relationship between the side lengths of triangle ? For a hint, type "Give me a hint!" and click "check my answer"
Pause here: Check with your teacher to make sure you got the correct answer for Task 7.
Congratulations! You just found the Pythagorean Identity. It true for all values of , and we can use it to solve various problems.