The Pythagorean Theorem
If a and b are the lengths of the legs of a right triangle and c is the length of the hypotenuse, then the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse. This relationship is called the Pythagorean Theorem and can be represented by the formula:
a2 + b2 = c2
See the video below to learn more about The Pythagorean Theorem, like how to solve for unknown side lengths of right triangles.
See the video below to learn more about The Pythagorean Theorem, like how to solve for unknown side lengths of right triangles.
After engaging with the Pythagorean Theorem Video take a look at the applet below.
Play around with the applet.
You can change the leg lengths by clicking and dragging A and B
What are some things you notice?
What do a, b, and c represent?
What do you think each of the colored boxes represent?
What do you notice about the math to the right?
Another Helpful Visual
Let's use what we have learned so far to practice solving a few problems!
Find the value of x in the right triangle below
Find the value of c in the right triangle below
Solve for y in the triangle below
What do you think you might do to solve for the value of x in this problem with the isosceles triangle? Share any thoughts you have in the textbox below.
Solve for the x value of the isosceles triangle above.
Need a hint?
The vertical dashed line that drops is cutting the triangle in half!
This means:
- The two triangles are the same
- They are both right triangles
- The bottom leg length of 6 is divided into 2 equal lengths for the two new triangle legs
Resources:
https://www.montereyinstitute.org/courses/DevelopmentalMath/COURSE_TEXT2_RESOURCE/U07_L1_T4_text_final.html
https://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-geometry/cc-8th-pythagorean-theorem/e/use-pythagorean-theorem-to-find-side-lengths-on-isosceles-triangles
https://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-geometry/cc-8th-pythagorean-theorem/e/pythagorean_theorem_1