Class 9 Math: Introduction to Euclid's Geometry Important Exam Questions

NexPro Tools Mathematics TeamJune 5, 20266 min read

Preparing for school exams or final CBSE boards requires practicing questions patterned after official grading schemes. We have compiled a list of crucial questions for Class 9 Introduction to Euclid's Geometry to help you test your mastery.

Exam-Pattern Questions and Answers

Question 1 (MEDIUM)

In the given figure, if 2 = 4 and 4 = 1, then using Euclid’s axiom prove that 1 = 2.

This is a descriptive problem. Work out all steps on paper before checking the solution.

Solution Explanation & Steps: Given: 2 = 4 and 4 = 1, using Euclid’s axiom, things which are equal to the same thing are equal to one another. Hence, 2 = 4 = 1 1 = 2 Hence proved.

Question 2 (MEDIUM)

Does Euclid’s fifth postulate imply the existence of parallel lines? Explain.

This is a descriptive problem. Work out all steps on paper before checking the solution.

Solution Explanation & Steps: If straight line l falls on two straight lines m and n such that the sum of interior angles on same side of l is 180°, then by Euclid’s 5th postulate the lines will not meet on this side of l. Also, the sum of interior angles on other side of l will be 180°, they will not meet on the other side also. ⇒ m and n never meet ⇒ m and n are parallel.

Question 3 (HARD)

Prove that "If two lines intersect each other, then the vertically opposite angles are equal." Using this theorem, find all the angles if ∠ POR : ∠ ROQ = 5 : 7 in the below figure where lines PQ and RS intersect each other at point O.

This is a descriptive problem. Work out all steps on paper before checking the solution.

Solution Explanation & Steps: Given, To Prove, Figure - 1½ marks Proof - - 1½ marks ∠ POR +∠ ROQ = 180° (Linear pair of angles) But ∠ POR : ∠ ROQ = 5 : 7 (Given) Therefore, ∠ POR = 5/12 × 180° = 75° Similarly, ∠ ROQ = 712 × 180° = 105° Now, ∠ POS = ∠ROQ = 105° (Vertically opposite angles) and ∠ SOQ = ∠POR = 75° (Vertically opposite angles) SECTION - E(Case Study Based Questions) Questions 36 to 38 carry 4 marks each.

Grading Step-Marking Guidelines

Remember that teachers award partial marks for writing down formulas, stating the given variables, and drawing diagrams. Never leave a question blank on an exam. Write down the relevant formulas and initial substitution steps to secure partial credits.

📚 Class 9 Math Resource Hub for Introduction to Euclid's Geometry: • 🧮 Interactive Solver: Solve Introduction to Euclid's Geometry Problems - Verify steps in real-time. • 📝 Timed Practice Quiz: Take Introduction to Euclid's Geometry Online Quiz - Test your speed and concepts. • 📄 Printable Worksheet: Download Introduction to Euclid's Geometry PDF Worksheet - Interactive problems with answers. • 📐 Formula Sheet: View Introduction to Euclid's Geometry Key Equations - Complete revision references. • 🔄 Next Topic Guide: Lines and Angles Study Notes • 🎓 Syllabus Overview: Class 9 Mathematics Portal - Access all chapter guides.
Back to Blog PortalGo to Homepage