Propositions and Converses Class 9 Maths Worksheet with Quiz and Activities
Test claims, write converses and hunt for counterexamples, with a chart of n squared + n + 11 you build in 2D and 3D. On WitKnowLearn you get the Propositions and Converses Class 9 online quiz, online activities and interactive games, a logic lab, a virtual lab and a worksheet-style practice sheet for NCERT Ganita Manjari Chapter 9.
Propositions and Converses Class 9 Online Quiz
20 questions: 10 easy, 5 average and 5 thinking. Tap an answer and the next question comes up.
Propositions and Converses Class 9 Activities
👆 Tap a tab to switch: Learn, Games, Labs, Challenges, Virtual Lab and Practice sheet
Propositions and Converses: the Story of Reasoning
A short read for Class 9 before you play. These notes follow Chapter 9 of NCERT Ganita Manjari, Part I.
❓ Propositions
A proposition is a statement that is true or false.
➡ If-then
Many statements have the form: if P, then Q.
🔁 Converses
The converse swaps the parts: if Q, then P.
❌ Counterexamples
One case that fails proves a statement false.
📐 Proofs
A proof shows a statement is true in every case.
📜 History
Fermat guessed a pattern and Euler found it fails.
Propositions and Converses Class 9 Activities
Test claims on the Number Train. Earn up to 3 stars in every activity.
This page follows NCERT Class 9 Maths Ganita Manjari, Part I, Chapter 9. Students write converses, hunt for counterexamples and check proofs.
The activities are pitched at Class 9 level. Students sort propositions, pop true facts, test patterns like n squared + n + 11, and solve case studies on sticks, triangles and divisibility. The virtual lab builds a chart of n squared + n + 11 in 2D bars and 3D towers until the counterexample appears. Explore more Class 9 maths worksheets on WitKnowLearn after this chapter.
Formulas and facts to know
| Statement | Converse | Converse true? |
|---|---|---|
| x = y gives x cubed = y cubed | x cubed = y cubed gives x = y | Yes |
| Multiple of 6 gives multiple of 3 | Multiple of 3 gives multiple of 6 | No, 9 |
| Congruent gives equal area | Equal area gives congruent | No |
| Divisible by 3 and 4 gives by 12 | Divisible by 12 gives by 3 and 4 | Yes |
How to use this page
- Flip the six cards and try the Logic Lab in the Learn tab.
- Play the five games and the five labs to practise each idea.
- Finish the five challenges to collect up to 15 points.
- Build the counterexample chart of n squared + n + 11 in the Virtual Lab and see it in 2D and 3D.
- Take the 20-question online quiz, with assertion and reason and case study questions, and fill in the practice sheet.
Worked examples
"If a number is divisible by 4, then by 8". False: 12.
400 + 441 = 841 = 29 squared, so yes.
No. n = 10 gives 121 = 11 x 11.
This Propositions and Converses worksheet for Class 9 maths gives you online activities and interactive games that make the chapter clear. Every activity has a goal, a hint and a short fact, so students learn while they enjoy.
Complete Guide: NCERT Class 9 Maths Propositions and Converses Chapter 9
This guide is for Class 9 students, parents and teachers. It covers Chapter 9 of NCERT Ganita Manjari, Part I, and shows how to use the quiz, labs and games on this page.
Introduction to Propositions and Converses
The chapter studies statements, if-then reasoning, converses and counterexamples, and why proof matters in mathematics.
What is there in this chapter
- What is a proposition.
- If-then statements.
- Converse of a statement.
- Counterexamples.
- Proving statements.
- Divisibility rules as if-then statements.
- Converse of the Baudhayana-Pythagoras theorem.
Learning objectives
- Tell propositions from other sentences.
- Write the converse of a statement.
- Find counterexamples.
- Prove short statements.
- Reason with assertions and case studies.
Learning outcomes
- The student can write the converse of an if-then statement.
- The student can find that n = 10 disproves n squared + n + 11.
- The student can check that 20, 21, 29 is a right triangle.
- The student can solve a case study on sticks as diagonals.
Propositions and Converses Class 9 resources on this page
| Resource | What it gives |
|---|---|
| Online quiz | 20 questions: 10 easy, 5 average and 5 thinking, with assertion and reason and case study questions and a full review |
| Flip cards | 6 picture cards with one-line rules |
| Logic Lab | A hands-on lab with 3 rounds |
| Games | 5 interactive games |
| Labs | 5 activity labs |
| Virtual Lab | 2 experiments and a 2D and 3D counterexample chart builder with aim, procedure, observations and conclusion |
| Challenges | 5 challenges, 15 points in all |
| Practice sheet | A worksheet-style sheet with 16 questions, name and date lines and a live score |
Key facts
| Idea | Rule |
|---|---|
| Proposition | True or false |
| Converse | Swap if and then |
| Counterexample | One failing case |
| Perfect square | Odd number of factors |
| 3 and 4 | LCM 12 |
| Equal areas | Not always congruent |
Types of questions you may see
- Write a converse.
- Find a counterexample.
- Test a pattern for many values.
- Divisibility and factors.
- Assertion and reason questions.
- Case studies on triangles and sticks.
Solved examples
If the road is wet, it rained.
9.
121.
n = 11.
Yes.
4.
Common mistakes
| Mistake | Correct idea |
|---|---|
| Thinking many examples prove a statement. | Only a proof does. One counterexample disproves it. |
| Assuming the converse is true. | Test it separately. |
| Calling a question a proposition. | A proposition is true or false. |
| Using 4 and 6 to test divisibility by 24. | They share a factor, so the LCM is 12. |
| Treating "false" as "not a proposition". | A false statement is still a proposition. |
Propositions and Converses in daily life
Courts, science and computer programs all depend on clear if-then statements and on spotting counterexamples.
Tips for parents and teachers
- Write the converse of every if-then statement you meet.
- Try small numbers first when hunting for a counterexample.
- Check the converse of a proof separately.
- Practise one assertion and one case study each week.
Related Class 9 Maths Worksheets
- 🔢Number Systems Class 9 Worksheet
- 🧮Polynomials Class 9 Worksheet
- 📍Coordinate Geometry Class 9 Worksheet
- 📈Linear Equations in Two Variables Class 9
- 📐Introduction to Euclids Geometry Class 9
- 📏Lines and Angles Class 9 Worksheet
- 🔺Triangles Class 9 Worksheet with MCQs
- 🔷Quadrilaterals Class 9 Worksheet
- ⭕Circles Class 9 Worksheet with MCQs
- 🧩Herons Formula Class 9 Worksheet
- 📦Surface Area and Volumes Class 9 Worksheet
- 📊Statistics Class 9 Worksheet
Propositions and Converses Class 9 FAQs
What is Chapter 9 of NCERT Class 9 Maths Ganita Manjari?
Chapter 9 is Propositions and their Converses. It covers statements that are true or false, if-then reasoning, converses, counterexamples and short proofs.
What is a proposition?
A proposition is a statement that is either true or false. "7 is an even number" is false but still a proposition. Questions, commands and exclamations are not propositions.
What is the converse of a statement?
The converse of "If P then Q" is "If Q then P". The converse of "If it rains, then the road is wet" is "If the road is wet, then it has rained".
Is the converse of a true statement always true?
No. "If a number is a multiple of 6, then it is a multiple of 3" is true, but its converse is false, because 9 is a multiple of 3 and not of 6.
What is a counterexample?
A counterexample is one case where the if part holds but the then part fails. One counterexample is enough to prove a proposition false.
Why is "n squared + n + 11 is always prime" false?
It gives primes for n = 1 to 9, but for n = 10 it gives 121 = 11 x 11. Many examples do not prove a statement, but one counterexample disproves it.
Is the converse of the Baudhayana-Pythagoras theorem true?
Yes. If a squared + b squared = c squared for the sides of a triangle, the triangle is right-angled. For 20, 21 and 29: 400 + 441 = 841 = 29 squared.
Which numbers have an odd number of factors?
Exactly the perfect squares. For example 49 has 3 factors: 1, 7 and 49.
Why does "divisible by 3 and 4 implies divisible by 12" work?
3 and 4 have no common factor, so their LCM is 12. But 4 and 6 share the factor 2, so their LCM is 12 and not 24.
Do equal areas make two triangles congruent?
No. A triangle with base 4 and height 3 and one with base 6 and height 2 both have area 6 but are not congruent. The converse is true: congruent triangles have equal areas.
Can both a statement and its converse be true?
Yes. "If x = y, then x cubed = y cubed" and its converse are both true, because every real number has one cube root.
What can students do on this page?
Students can take a 20-question online quiz with assertion and reason and case study questions, play five games, try five online activities, finish five challenges, run the Logic Lab, do two virtual experiments, build a counterexample chart in 2D and 3D, and fill in a 16-question practice sheet with a Show answers button.
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