NCERT Ganita Manjari, Class 9, textbook pages 1–7 (Part II)

How to help your child with Class 9 Maths Chapter 9, Propositions and their Converses, at home

Statements, converses and counterexamples, explained for parents: a 30-minute study session, a quick challenge, a 5-day plan and the mistakes to watch for.

P: if X then Yconverse: if Y then Xtrue P ≠ true converse

NCERT Class 9 Maths Chapter 9 Propositions and their Converses: what it teaches

A proposition is a statement that is true or false. Your teen learns “if X then Y” statements, their converses (“if Y then X”), why a true statement can have a false converse, and how one counterexample disproves a claim.

Why it matters later. Logical reasoning with converses underlies every proof in geometry and algebra from Class 9 onward.

See it: this chapter in pictures

P: if it rains, the road is wet ✓Q: if the road is wet, it rained✗ a tanker spilled water
One counterexample is enough.
two sides equal → base angles equaltwo angles equal → opposite sides equalboth true
Some converses are true.
even ⇒ divisible by 4?6 is even, not divisible by 4counterexample: false
Test claims with examples.

You need

  • paper and pencil
  • a ruler and protractor

Tonight’s 30 minutes

  1. “If it rains, the road is wet.” Write the converse. Is it true? (No: a tanker could wet the road.)
  2. Take: if a triangle has two equal sides, the opposite angles are equal. Write the converse and test it with drawings.
  3. Find a counterexample to: every even number is a sum of two even primes.
  4. List three maths statements whose converses are also true.

Words to use

  • proposition
  • converse
  • if … then
  • counterexample
  • implies
  • proof

Watch for

  • Assuming a converse is true because the original is. Test the converse separately; look for a counterexample.
  • Thinking examples prove a statement. Examples support it; only a proof shows it is always true.

What it sounds like at home

A short example of the conversation. Your words will differ; the questions are what matter.

YouIf the road is wet, did it rain?

Your childNot necessarily: a tanker could have spilled water.

A game for this week: Converse challenge

  1. One player states an if–then sentence.
  2. The other states the converse.
  3. Both decide if it is true, giving a counterexample if not.
  4. Swap roles.

A 5-day plan, 30 minutes a day

  1. Day 1Everyday if–then statements.
  2. Day 2Converses in geometry.
  3. Day 3Counterexamples.
  4. Day 4True statements with true converses.
  5. Day 5Converse challenge.

Everyday moments to practise

  • Advertising claims.
  • Rules and laws.
  • Medical tests.
  • Debates and arguments.

Quick check

Ask these at the end of the week. Tap to see the answer.

Converse of “If a number is divisible by 4, it is even”?

If a number is even, it is divisible by 4 (false: 6).

How many counterexamples disprove a claim?

One.

Converse of “If two sides are equal, opposite angles are equal” is true?

Yes.

Ready for the next chapter when your child…

  • Writes converses correctly.
  • Judges truth with proofs or counterexamples.
  • Explains why examples are not proofs.

Activities, wording and illustrations are Mathify Kids’ own, following the topics of NCERT’s Ganita Manjari (Class 9). See the full Class 9 parent guide for every chapter.

Questions parents ask

What is a proposition?

A statement that is either true or false.

What is a converse?

The statement with the ‘if’ and ‘then’ parts swapped.

Why learn this in maths?

Proofs depend on knowing exactly what is assumed and what follows.