Uvero — STEM Learning

The Converse of Pythagoras

If the square of the longest side equals the sum of squares of the other two, the triangle is right-angled. Test the longest side against $a^2+b^2$ . A careful solution names the quantities, keeps place value or units visible, and explains why each operation fits.

Worked reasoning

The longest side is 10.
$6^2+8^2=36+64=100=10^2$ .

Is a triangle with sides 6, 8 and 10 right-angled?

Yes

Not enough information

Only if isosceles

Which statement best captures the central mathematical idea in The Converse of Pythagoras?

Test the longest side against $a^2+b^2$ .

A familiar-looking calculation may be used without checking place value, units, conditions or what the answer represents.

A memorised formula is valid even when its conditions are not met.

The diagram or notation replaces the need to justify each mathematical step.

When starting a problem about The Converse of Pythagoras, which move is most reliable?

Represent the given information clearly and identify the operation or relationship required for the converse of pythagoras.

Round every value before identifying the mathematical structure.

Choose the longest available formula and substitute immediately.

Assume the desired conclusion and work backwards without checking equivalence.

Which statement is a misconception that must be rejected when working with The Converse of Pythagoras?

A familiar-looking calculation may be used without checking place value, units, conditions or what the answer represents.

Test the longest side against $a^2+b^2$ .

Represent the given information clearly and identify the operation or relationship required for the converse of pythagoras.

Estimate first, then reverse the operation or use a second representation to check that the answer is reasonable.