Introduction
HSA Notes brings short, clear, exam focused notes designed to help Class 9 SSC Part One Matric students score 90 plus marks in Punjab Board exams under the New Book 2026 to 2027 session. This page covers Unit 9, Similar Figures, from Exercise 9.1, 9.2, 9.3, 9.4 & Review Exercise including checking similar solids and triangles by their side ratios and using the scale factor to find missing side lengths.
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HSA Notes Features
- Short, easy to remember definitions.
- Step by step solutions for every question.
- Tricks and memory aids for faster revision.
- Exact alignment with the PCTB and PECTAA textbook.
- Similar figures simplified into a clear, repeatable method.
- Past paper pattern questions included throughout.
- A fast revision format built for last minute review.
- Trusted by Punjab students.
Available Across All Punjab Boards and Top Schools
These notes are built for students across all Punjab Boards, including Lahore, Gujranwala, Rawalpindi, Faisalabad, Bahawalpur, Multan, Sargodha, Sahiwal, and DG Khan, and are used at top schools including The City School, Beaconhouse, Roots International, Lahore Grammar School, Karachi Grammar School, Froebel’s, The Educators, Army Public School, Divisional Public School, and Government Model School.
Exercise 9.1, Q1, Similar Solids
The two given solids have sides of 3, 4, 5 units and 4.5, 6, 7.5 units. Dividing each side of the second solid by the matching side of the first gives 4.5/3, 6/4, and 7.5/5, which all simplify to 1.5. Since every pair of corresponding sides shares the same ratio, the solids are similar, with a scale factor of 1.5.
Exercise 9.1, Q2, Similar Triangles
Triangle ABC has sides 6, 9, and 12 units, and triangle DEF has sides 10.5, 15.75, and 21 units. Dividing each side of DEF by the matching side of ABC gives 10.5/6, 15.75/9, and 21/12, which all simplify to the same ratio, 3.5, equivalent to the ratio 2 : 3 : 4 between the two triangles in lowest terms. Because all three corresponding side ratios match, triangle ABC is similar to triangle DEF.
Exercise 9.1, Q3, Finding Missing Sides with the Scale Factor
Triangle ABC is similar to triangle DEF, with AB = 12 cm, AC = 20 cm, BC = 16 cm, and DE = 6 cm. Since DE corresponds to AB, the scale factor from triangle ABC to triangle DEF is DE divided by AB, which is 6/12, or 1/2. Applying this same scale factor to the remaining sides gives DF equal to AC multiplied by 1/2, which is 20 × 1/2 = 10 cm, and EF equal to BC multiplied by 1/2, which is 16 × 1/2 = 8 cm.
How to Check Whether Two Figures Are Similar
Two solids or triangles are similar when their corresponding sides all share the same ratio to one another, even though their actual sizes differ.
The reliable method is to divide each side of the second figure by its matching side in the first figure, one pair at a time, and compare the results. If every pair gives the same number, that number is the scale factor and the figures are similar.
If even one pair gives a different ratio, the figures are not similar, no matter how close the other ratios might be. Writing out each ratio as a fraction before simplifying, rather than estimating by eye, is the safest way to avoid mistakes when the numbers involve decimals.
How to Find a Missing Side Using the Scale Factor
Once two figures are known to be similar, any missing side in one figure can be found from its known counterpart in the other. First identify one pair of corresponding sides where both lengths are known, and divide the length in the target figure by the matching length in the reference figure to get the scale factor.
Then multiply every other known side of the reference figure by that same scale factor to find its corresponding missing side in the target figure. Keeping track of which side corresponds to which, based on the order of the letters in the similarity statement such as triangle ABC similar to triangle DEF, is essential, since matching the wrong pair of sides is the most common error on this type of question.
Why This Unit Matters for Your Overall Score
Similar figures build directly on ratio and proportion skills from earlier units and set up the reasoning used later in topics involving congruence, scale drawings, and real-world measurement problems such as finding heights or distances using shadows or maps.
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Being comfortable checking similarity through side ratios and then using a confirmed scale factor to solve for unknown lengths is a skill that recurs often in past papers, making this unit a reliable source of marks with the right method in place.
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Frequently Asked Questions
How do I check if two triangles are similar? Divide each side of one triangle by its corresponding side in the other triangle. If all three ratios are equal, the triangles are similar.
What is a scale factor? The scale factor is the constant ratio between the corresponding sides of two similar figures, found by dividing a side of one figure by the matching side of the other.
How do I find a missing side in a similar figure? Find the scale factor from a known pair of corresponding sides, then multiply the known side of the reference figure by that scale factor to get the missing side.
Are these notes aligned with the PCTB and PECTAA textbook? Yes, these notes are built to exactly match the PCTB and PECTAA New Book for Class 9 Mathematics for the 2026 to 2027 session.
Conclusion
With Exercise 9.1 fully solved, covering similar solids, similar triangles, and the use of the scale factor to find missing sides, Class 9 students have a strong foundation for Unit 9, Similar Figures. Use these notes alongside regular practice with past papers to build the confidence needed for 90 plus marks in your Punjab Board exam.
Best of luck for your Class 9 Mathematics exam!
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