Easy Steps to Solve Pythagorean Theorem Problems!

Are you excited to learn about the Pythagorean Theorem? This cool concept helps us solve problems with right triangles! Here are some simple steps to help you out!

1. Know the Theorem!
   The Pythagorean Theorem tells us that in a right triangle, the square of the longest side (called the hypotenuse or $c$) is equal to the sum of the squares of the other two sides (called $a$ and $b$). You can write this as:
   $c^2 = a^2 + b^2$

2. Check the Triangle Type!
   Before you start, make sure you have a right triangle. Look for the right angle, which is $90^\circ$. This step is super important!

3. Label the Sides!
   Name the sides of your triangle. Usually, we call the longest side $c$, and the other two sides $a$ and $b$. This makes it easier to understand what to do next!

4. Pick Your Method!

   • To Find the Hypotenuse: If you know the lengths of both other sides ($a$ and $b$), you can use this formula:
     $c = \sqrt{a^2 + b^2}$
   • To Find a Missing Side: If you know the hypotenuse ($c$) and one of the other sides ($a$), you can rearrange the formula like this:
     $b = \sqrt{c^2 - a^2}$

5. Do the Math!
   Now it’s time to do the calculations! Make sure to square the lengths of the sides and add or subtract them correctly to find the answer you need.

6. Double-Check Your Work!
   After you find your answer, plug it back into the original theorem to make sure it fits. Your solution should make the equation true!

Try These Practice Problems!

1. If you have a right triangle with sides of 3 cm and 4 cm, what is the length of the hypotenuse?
2. In a triangle where the hypotenuse is 10 cm and one side is 6 cm, what is the length of the other side?

Remember, practice makes perfect! Follow these steps with excitement, and soon you'll be a pro at the Pythagorean Theorem! Happy solving!