Geometry

Applying the Pythagorean Theorem to Non-Right Triangles

Students use a2+b2=c2a^2 + b^2 = c^2 on any triangle even when no angle is marked 90∘90^\circ.

Quick check

Why students make it

The formula looks like a general side-length rule because it is simple and familiar. Students may also assume the longest side is always a hypotenuse, but a hypotenuse exists only in a right triangle.

The rule done right

The Pythagorean Theorem applies only to right triangles, where aa and bb are the legs and cc is the hypotenuse. For a non-right triangle, use the Law of Cosines, c2=a2+b2−2abcos⁡Cc^2 = a^2 + b^2 - 2ab\cos C, or another appropriate triangle rule.

Related resources

pythagorean-theoremright-triangleslaw-of-cosines