FORMULABANK

Pythagoras theorem can be used to check if a triangle is right-angled. This requires knowing all the side lengths. If the side lengths of a triangle satisfy the equation:

$a^2+b^2=c^2$

Then we know that the triangle is right-angled.

Sketches of triangles

Example of calculation:

Triangle 1:

$3{+}^2+4{+}^2=25$
$5^2=25$

Since both the left and right sides of Pythagoras theorem ($a{2}^{}+b{2}^{}=c{2}^{}$) result in 25, we know that Pythagoras theorem holds for Triangle 1. This means that Triangle 1 is right-angled.

Triangle 2:

$32^{}+4.032^{}=25.2409$
${4.72}^2=22.2784$

Since $a{2}^{}+b{2}^{}$ is not the same as $c{2}^{}$, Triangle 2 is NOT right-angled.

Triangle 3:

$22^{}+12^{}=5$
${2.15}^2=4.6225$

Since $a{2}^{}+b{2}^{}$ is not the same as $c{2}^{}$, Triangle 3 is NOT right-angled.