Propositions and their Converses
Class 9 · Mathematics
3 ideas in Class 9 Mathematics, explained in plain words, with games and quizzes to practise.
Propositions and Converses
Part of: Propositions and Converses
A proposition is a statement that is either true or false. To form its converse, exchange the “if” part and the “then” part.
Why it matters. A true statement does not guarantee that its converse is true, so checking both directions matters.
Try it in two minutes
- Write a simple if-then statement.
- Swap its condition and conclusion.
- Ask whether the new statement must always hold.
Try at home. Try reversing a familiar rule and look for a case that tests it.
Truth, Proofs and Counterexamples
Part of: Truth, Proofs and Counterexamples
A proof supports a claim for every allowed case. One counterexample is enough to disprove a claim that says something is always true.
Why it matters. Counterexamples make false claims easier to spot and help clarify what a proof must establish.
Try it in two minutes
- Read a claim that uses “all” or “every”.
- Test a few cases.
- If one case fails, explain why it disproves the claim.
Try at home. Invent a counterexample to a rule that sounds true at first.
Geometric Statements in Both Directions
Part of: Geometric Statements in Both Directions
Geometry claims often connect a property with a conclusion. Checking the converse means deciding whether the conclusion alone guarantees the original condition.
Why it matters. This prevents assuming that a property works in both directions when only one direction has been established.
Try it in two minutes
- Sketch a shape satisfying a stated property.
- Draw a different shape with the proposed converse property.
- Compare whether the conclusion forces the original condition.
Try at home. Use quick sketches to test a geometric converse.
What your child will practise
- Geometric Statements in Both Directions: Candy Quick Fire (Quick Fire)
- Geometric Statements in Both Directions: Ocean Puzzle (Clue Puzzle)
- Propositions and Converses: Desert Quick Fire (Quick Fire)
- Propositions and Converses: Number Sort (Sort It Out)
- Truth, Proofs and Counterexamples: Mission Control Quest (Collect the Answer)
- Quiz: Geometric Statements in Both Directions (8 questions)
- Quiz: Propositions and Converses (8 questions)
- Quiz: Truth, Proofs and Counterexamples (8 questions)