The converse reverses the theorem: if the square of the longest side equals the sum of the squares of the other two sides, the triangle is right-angled. First identify the longest side; do not decide by the drawing. Example A triangle has sides 7 cm, 24 cm and 25 cm. 72+242=625=252, so it is right-angled opposite the 25 cm side. For sides 6 cm, 8 cm and 11 cm, 62+82=100 121=112; this triangle is not right-angled. Check that the lengths can form a triangle: the sum of the two shorter sides must exceed the longest side. An approximate equality based only on rounded measurements is evidence of an approximately right angle, not an exact proof.

The converse reverses the theorem: if the square of the longest side equals the sum of the squares of the other two sides, the triangle is right-angled. First identify the longest side; do not decide by the drawing.

A triangle has sides 7 cm, 24 cm and 25 cm. \(7^2+24^2=625=25^2\), so it is right-angled opposite the 25 cm side. For sides 6 cm, 8 cm and 11 cm, \(6^2+8^2=100\ne121=11^2\); this triangle is not right-angled.

Check that the lengths can form a triangle: the sum of the two shorter sides must exceed the longest side. An approximate equality based only on rounded measurements is evidence of an approximately right angle, not an exact proof.

Testing for a right angle

Testing for a right angle