Converse Pythagorean Theorem Calculator

Q: What is the converse of the Pythagorean theorem?

It says that if three side lengths satisfy a² + b² = c², then the triangle is a right triangle.

Q: Which side should be c?

Use the longest side as c. The checker sorts the three inputs before comparing the squares.

Q: Can this checker solve a missing side?

No. This page checks three known side lengths. Use the main Pythagorean calculator when one side is missing.

a² + b² ? c²

Enter three side lengths to check the converse of the Pythagorean theorem and see whether the triangle is right, acute, obtuse, or invalid.

The converse test sorts the three sides, treats the longest side as c, and compares a² + b² with c².

Check Three Sides

Enter any three side lengths. The checker sorts them and uses the longest side as c.

Side 1

Side 2

Side 3

Result

a² + b² ? c²

Enter three sides to compare the squares.

Converse rule

If a² + b² = c² after sorting the sides, the triangle is right. If the values are not equal, the triangle is not right.

What the converse theorem checks

Step 1

Sort the sides

The longest valid side becomes c because the hypotenuse is always the longest side in a right triangle.

Step 2

Compare squares

Square the two shorter sides and compare their sum with the square of the longest side.

Step 3

Classify the triangle

Equality proves a right triangle. A larger or smaller sum classifies acute or obtuse triangles.

?How to read the result

Right triangle

a² + b² = c²

The converse proves the triangle has a 90° angle.

Right

Acute triangle

a² + b² > c²

All angles are less than 90°.

Acute

Obtuse triangle

a² + b² < c²

One angle is greater than 90°.

Obtuse

Converse FAQ

Q1.What is the converse of the Pythagorean theorem?