What is the Pythagorean Theorem?

What is the Pythagorean Theorem?

1. Right Triangle

   • Is basically a triangle with one right angle (90 degree angle). That is why it is called the right triangle.
   • There are three sides to make a triangle, and two side connected to a perpendicular.
   • When drawing a right triangle, to check it has a right angle, use a protractor to measure the angle. Than, draw a box in the corner to show that it is a 90 degree angle.

2. Leg of Right Triangle

   • The legs of the right triangle are two sides that intersect. They than determine the right angle.
     • These sides are usually called legs, or referred to as 'a' and 'b'. Usually the side that is the shortest is 'a' and the side that is the second longest (longest side is hypotenuse).

3. Hypotenuse

   • The hypotenuse is a side of the right triangle and it is opposite of the 90 degree angle.
   • The longest side of the right triangle.
   • This side of the shape (the yellow question mark side) is called the hypotenuse, and is usually recognized as 'c'.

4. Relationships between Right Triangle, Leg of Right Triangle, Hypotenuse, Area, Base, Height & Squares

   • a (squared) + b (squared)= c (squared)
     • a= leg (side a)
       • b= leg (side b)
       • c= hypotenuse (side c)
     • RULE:
       • a + b= c
   • One right angle triangle can create three squares. The area of the square created by side a of the triangle, plus the area of the square created by side b of the triangle, will equal the area of the square created by side c of the triangle.
     • You have to find the area of side 'a' and 'b', than adding those areas together, you will get the area of the biggest and final square of the hypotenuse.
     • You use the rule for Pythagorean Theorem so that you can figure out the missing side lengths of a right triangle. You may need to add or subtract areas to get your answer. The rule states that if you know two out of three side lengths of a right triangle, you can use the relationship of the area of the squares created by the side lengths, to determine the one missing side length. Finding the area means you found the side length.

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