What is the Pythagorean theorem?

Question

Accepted Answer

In a right triangle, a² + b² = c², where c is the hypotenuse. The Pythagorean theorem states that in a right triangle, the sum of the squares of the two shorter sides (legs) equals the square of the longest side (hypotenuse): a² + b² = c². This relationship allows us to find any side of a right triangle when the other two sides are known.

The fact that the sum of angles in any triangle is 180 degrees is the triangle angle sum theorem, not the Pythagorean theorem; it applies to all triangles, not just right triangles. The formula for the area of a circle (πr²) is a geometric formula but has no direct connection to the Pythagorean theorem or right triangles. The statement that parallel lines never intersect is a postulate of Euclidean geometry, not a theorem about right triangles.

The Pythagorean theorem is one of the most important geometric relationships tested on the DSST exam. Students should be able to apply it to find missing side lengths, verify whether a triangle is a right triangle, and recognize common Pythagorean triples (3-4-5, 5-12-13, 8-15-17). The theorem has applications throughout mathematics and science.

DSST Math for Liberal Arts: Question of the Day

Get a free DSST Math for Liberal Arts question every day

Ready for the full DSST Math for Liberal Arts? Earn 3 college credits.