Converse of Pythagoras theorem
If the square of the longest side of a triangle equals the sum of the squares of the other two sides, the triangle is right-angled.
Practice This ConceptMain explanation
Teacher explanation
This is the reverse test. You first pick the longest side, then check the square relation to decide whether a right angle is present.
Example
For sides 5 cm, 12 cm, and 13 cm, 13² = 5² + 12², so the triangle is right-angled.
Simple analogy
Longest side, then square check.
Common confusion
Students sometimes check the wrong side or forget that the largest side must be treated as the hypotenuse.
Exam tip
Always start with the longest side when using the converse.
Answer writing and exam use
1-mark use
Write the exact meaning of converse of pythagoras theorem in one clean line.
2-mark use
Define converse of pythagoras theorem and add one example or condition.
3-mark use
Explain converse of pythagoras theorem, show the method or example, and mention the common mistake.
Practice this concept with focused MCQs
Open the concept quiz intro first, review the test details, and then start a focused MCQ set from this concept only. Instant score and answer review are live now.
Help improve this page
Found something confusing, incorrect, or missing?