What it does
Many facts in maths have the form “if P, then Q”: if a quadrilateral is a square, then its diagonals are equal. Swap the two parts and you get the converse, “if Q, then P”: if a quadrilateral has equal diagonals, then it is a square. The converse of a true statement can be true or false, and this page lets you find out by experiment.
- Pick one of 12 statements about quadrilaterals, triangles, angles and whole numbers.
- Choose Test the statement or Test the converse; the “if” and “then” parts are shown separately.
- Make random figures one at a time, with their sides, angles and diagonals measured, and see whether each one agrees.
- Hunt through 100 or 1 000 random cases for a counterexample: a case where the “if” part is true and the “then” part is false. One counterexample proves a statement false.
It follows the Class 9 maths chapter on propositions and their converses (statements, proof and counterexamples).
The quadrilateral facts are easier to see by dragging corners in the quadrilateral explorer; the converse of Pythagoras’ theorem is proved in pythagoras proof playground, and if-then logic itself is in the logic simplifier.
How to use it
- Choose a Statement.
- Press Test the converse to swap the parts (or stay on the statement).
- Press New random figure a few times. Under the picture you get the measurements and two answers: is the “if” part true, and is the “then” part true? A figure where the “if” part is false tells you nothing, so try another.
- Press Test 100 or Test 1 000. The page reports how many cases met the “if” part, and whether any broke the “then” part. If it finds a counterexample, Draw the counterexample shows it in a warning colour.
- Open Show the answer and the reason to check yourself.
A worked example
Take “If a quadrilateral is a square, then its diagonals are equal.” Every square the page makes has equal diagonals, so the hunt finds no counterexample. The converse is “If a quadrilateral has equal diagonals, then it is a square.” Hunt 1 000 figures: about a third have equal diagonals (squares, rectangles, isosceles trapeziums) and the page soon draws a rectangle with diagonals of the same length that is not a square. So the converse is false.
Now take “If a quadrilateral is a parallelogram, then its diagonals bisect each other.” Both it and its converse survive every hunt, and both can be proved, so it can be stated as one fact: a quadrilateral is a parallelogram if and only if its diagonals bisect each other.
Tips
- Random testing is evidence, not proof: a true direction needs a proof, but a false one needs only one counterexample.
- Shapes are checked by measuring, the way you would with a ruler and protractor, to a tiny tolerance.
- Some families (rectangles, kites, isosceles trapeziums) are made on purpose so that the interesting cases turn up often.
Check yourself
Four fresh true-or-false questions each time: three converses and one statement. Type true or false (or t / f) and press Check. Nothing is saved.
FAQ
Is “if P then Q” the same as “if not Q then not P”? Yes. That is the contrapositive, and it is always true when the statement is. The converse is different.
Is this from the NCERT book? It covers the same topic with fibub’s own statements and figures. fibub is not part of NCERT.
Where the numbers come from
- The statements are standard school geometry and number facts (properties of parallelograms, rhombuses, rectangles and isosceles triangles, Pythagoras' theorem and its converse, divisibility). Written for fibub; the figures are random.
- Checked by testing every true direction on 3 000 random figures with no counterexample, and finding a counterexample for every false converse (rectangle, kite, parallelogram, 9).
Standard scientific values, such as constants, atomic weights and melting points, are facts found in every textbook; we name where ours were checked. If you are an author or publisher and want a value, a credit or a table changed or removed, tell us and we will act quickly.
Last updated 2026-11-09.