Pythagorean Theorem “Formula/Reference” Sheet – Johnsen Math 8
The Pythagorean Theorem states that A2 + B2 = C2
It can be simplified to find simply “C” by stating that √𝐴2 + 𝐵2 = C
This means or states that the hypotenuse of ANY RIGHT triangle can be found by calculating
the square root of the sum of the other 2 legs of the triangle.
There are a few special triangles that are helpful.
3-4-5 The legs are 3 and 4 (or the same multiple of 3 and 4)
The hypotenuse will always be 5 (or that multiple of 5).
5-12-13 The legs are 5 and 12, the Hypotenuse will always be 13 (or proportional to it).
The Pythagorean Theorem can be reversed to find a missing “leg” if given the other leg and
the hypotenuse: C2 – B2 = A2 OR C2 – A2 = B2
You MUST subtract FROM the hypotenuse to find the other leg.
Distance between 2 points on the coordinate plane using the Pythagorean Theorem:
Use your X and Y slope values: the distance from x1 to x2 and the distance from y1 to y2.
We see that the distance from Y1 to Y2 is 7 and the distance from X1 to X2 is 5.
The distance from (3,2) to (8,9) is √52 + 72 or √25 + 49 or √74
This equals either estimated at ~8.6 or just leave it as √74 (the exact value radical form)
Subtract your two X values.
Subtract your two Y values.
Find the distance using the Pythagorean Theorem.