Pythagorean Theorem - Converse - How to Use it
Pythagorean Theorem - Converse - How it Works - Video
Example 1
Example 1:
To use the Converse of the Pythagorean Theorem, we must look at the side lengths. We need to square the two smaller side lengths and compare it to the square of the longest side.
So we use the Pythagorean Theorem ==> a2 + b2 = c2 and substitute each number into the theorem ==> 122 + 82 = 142.
Next we square all the numbers ==> 144 + 64 = 196.
Then we add 144 and 64 ==> 208.
Now we have 208 ≠ 196. Since the 208, or the sum of the squares of the two smaller sides is greater than square the longest side, we have an acute triangle.
Also, if we joined the red and green angles, and put the blue angle on top of those two angles, the combine total of the two smaller angles is greater than the blue angle. This is another reason that all the angles are acute.
Example 2
Example 2:
To use the Converse of the Pythagorean Theorem, we must look at the side lengths. We need to square the two smaller side lengths and compare it to the square of the longest side.
So we use the Pythagorean Theorem ==> a2 + b2 = c2 and substitute each number into the theorem ==> 122 + 92 = 152.
Next we square all the numbers ==> 144 + 81 = 225.
Then we add 144 and 64 ==> 225.
Now we have 225 = 295. Since the 225, or the sum of the squares of the two smaller sides is equal to than square the longest side, we have a right triangle.
Also, if we joined the red and green angles, and put them on top of the blue angle, the combine total of the two smaller angles overlaps than the blue angle perfectly. This is another reason that all the angles are acute.
Example 3
Example 3:
To use the Converse of the Pythagorean Theorem, we must look at the side lengths. We need to square the two smaller side lengths and compare it to the square of the longest side.
So we use the Pythagorean Theorem ==> a2 + b2 = c2 and substitute each number into the theorem ==> 102 + 82 = 142.
Next we square all the numbers ==> 100 + 64 = 196.
Then we add 100 and 64 ==> 164.
Now we have 164 ≠ 196. Since the 164, or the sum of the squares of the two smaller sides is less than square the longest side, we have an obtuse triangle.
Also, if we joined the red and green angles, and put the blue angle on top of those two angles, the combine total of the two smaller angles is less than the blue angle. This is another reason that all the angles are obtuse.